TAKEOFF FUNDAMENTALS
Takeoff is a critical flight phase, one which constitutes only about one percent of total flight time, but
which results in about to 1/5 (20%). of all accidents. In high performance, high speed airplanes, such
accidents routinely involve serious damage and often result in fatalities. (Landing is an equally brief, even
more critical flight phase, where about 1/4 (25%) of all accidents occur.)
We will examine five factors which affect three important takeoff parameters. The three takeoff
parameters are:
1.
2.
3.
Takeoff distance X (distance covered from brake release to liftoff).
Take off time t (elapsed time from brake release to liftoff).
Takeoff speed V (liftoff speed).
The five factors are:
1. Changes in Gross Weight.
2. Changes in Density Altitude.
3. Changes in Temperature.
4. Runway Wind Changes.
5. Variation of Runway Slope from Horizontal.
We also give a real world example of how to compute takeoff distance using a takeoff performance chart
for a single engine high performance Navy jet airplane. Finally, we briefly discuss the importance of a
takeoff acceleration check and the hazard associated with premature rotation.
1. Theoretical Effects of Changes in Gross Weight, Density Altitude, Wind,
and Runway Slope on Liftoff Speed, Takeoff Distance, and Takeoff Time
During takeoff, thrust overcomes drag and tire friction forces to accelerate the airplane. We first examine
equations which allow predicting takeoff roll, speed, and time changes when gross weight, density altitude,
temperature, runway slope, or the headwind component changes
An increase in gross weight, temperature, or runway upslope, or a decrease in density altitude or headwind
component, causes an increase in one or more of takeoff speed, distance, and time. Sometimes the increase
can be drastic, especially when rising temperatures and higher takeoff elevations (density altitudes) lead to
significantly lower air density.
For example, later we will discuss a single engine jet airplane whose takeoff roll (at fixed gross weight)
increases from 2500’ to 10500’ when runway temperature rises from 0 o to 40o C, pressure altitude
decreases from sea level to 2000’, and headwind decreases from 25 kts to 0 kts. This is an increase of
420% in takeoff distance.
Implications of Equations for Rectilinear Motion. From basic physics, we know that
VF2 = VI2 + 2aX, and
VF = VI + at,
where VI and VF respectively are initial and final velocity in ft/sec; a is acceleration in ft/sec 2, assumed to
be constant (a naïve but useful assumption); X is distance traversed in feet; and t is time in seconds.
Applied to airplane takeoff, VF is liftoff velocity, VI = 0, X is takeoff roll, and we have
VF2 = 2aX, and VF = at, or
X = VF2 / 2a, and t = VF / a.
Rogers’s AS310 Notes, Part III: Page 1
These equations tell us that:


Takeoff roll X is directly proportional to the square of liftoff speed and inversely proportional
to acceleration:
X  V2 / a.
Takeoff time t is directly proportional to liftoff speed and inversely proportional to
acceleration.
t  V / a.
Suppose a change in some factor such as gross weight or density altitude causes a change in liftoff speed
and aircraft takeoff acceleration. Let X1, t1, and V1 be takeoff parameters associated with the initial
situation, and X2, t2 and V2 be parameters associated with the new situation. Then from the foregoing we
may conclude:
X 2 V22 a 1
t
V a

, and 2  2 1
X 1 V12 a 2
t 1 V1 a 2
Note: since these identities involve ratios, we may use airspeed in knots without bothering to convert to
ft/sec. Also, since we assume constant acceleration in both cases (when actually acceleration decreases
significantly during the takeoff roll), the error introduced is not as great as one might expect.
Effect of Changes in Gross Weight. Suppose gross weight changes from W1 to W2. Then, as we already
know, respective liftoff speeds V1 and V2 are given by
V2 / V1 =  (W2 / W1), or V22 / V12 = W2 / W1.
Also, from F = m a = (W/g) a, we see that at takeoff thrust F, acceleration is inversely proportional to gross
weight. We may conclude that the respective accelerations a 1 and a2 corresponding W1 and W2 are given
a
W
by 1  2 . (The equation says the acceleration is inversely proportional to weight.) Thus
a 2 W1
2
X 2 V22 a 1 W2 W2  W2 
t
V a
 , and 2  2 1 



X1 V12 a 2 W1 W1  W1 
t 1 V1 a 2
W2 W2  W2 


W1 W1  W1 
3/ 2
.
That is:



V2 = V1  (W2 / W1).
X2 = X1 (W2 / W1)2.
t2 = t1 (W2 / W1)3/2.
Expressed in English, these equations say that if takeoff gross weight changes from W 1 to W2:



Liftoff speed changes as the square root of (W 2 / W1).
Takeoff roll changes as the square of (W2 / W1).
Takeoff time changes as (W2 / W1) raised to the 3/2 = 1.5 power.
Rogers’s AS310 Notes, Part III: Page 2
Effect of Changes in Field Elevation (Jet or Normally Aspirated Prop). Suppose density ratio
corresponding to field elevation changes from 1 to 2. Then, as we already know, respective liftoff speeds
V1 and V2 are given by
V2 / V1 =  (1 / 2), or V22 / V12 = 1 / 2.
Also, from F = m a = (W/g) a, we see that at takeoff gross weight W, acceleration is directly proportional to
thrust F. Assuming thrust is proportional to density ratio for a jet or normally aspirated prop aircraft, we
a

may write 1  1 . (The equation says that acceleration is inversely proportional to density ratio.) Thus
a 2 2
2
X 2 V22 a 1 1 1  1 
t
V a
1  1  1 
 , and 2  2 1 

 2

 

X1 V1 a 2  2  2   2 
t 1 V1 a 2
 2  2   2 
That is, for a turbojet or normally aspirated reciprocating prop airplane:



3/ 2
.
V2 = V1  (1 / 2).
X2 = X1 (1 / 2)2.
t2 = t1 (1 / 2)1.5.
Expressed in English, these equations say that if density ratio changes from 1 to 2:



Liftoff speed changes as the square root of (1 / 2).
Takeoff roll changes as the square of (1 / 2).
Takeoff time changes as (1 / 2) raised to the 1.5 power.
Effect of Temperature Change at Fixed Pressure Altitude (Jet or Normally Aspirated Prop). Air
density is a function of pressure and temperature, as implied by the well-known relation  =  / . That is,
for a fixed pressure altitude (fixed field elevation and altimeter setting),   1 / . Thus the equations
given previously for density altitude change may be rewritten to reflect change in temperature at fixed
static pressure as follows:



V2 = V1  (2 / 1).
X2 = X1 (2 / 1)2.
t2 = t1 (2 / 1)1.5.
Recall that temperature ratio  must be calculated using absolute temperatures. Let TA represent absolute
temperature, with TA0 denoting SL temperature in a standard atmosphere. (To calculate TA, add 273 to
temperature in degrees Celsius, or 460 to temperature in degrees Fahrenheit.) Then 2 = TA2 / TA0, and 1
= TA1 / TA0, so 2 / 1 = TA2 / TA1. Thus the above equations may be rewritten:



V2 = V1  (TA2 / TA1).
X2 = X1 (TA2 / TA1)2.
t2 = t1 (TA2 / TA1)1.5.
Expressed in English, these equations say that if absolute temperature changes from TA1 to TA2:



Liftoff speed changes as the square root of (TA2 / TA1).
Takeoff roll changes as the square of (TA2 / TA1).
Takeoff time changes as (TA2 / TA1) raised to the 1.5 power.
Rogers’s AS310 Notes, Part III: Page 3
Effect of Headwind. The effect of a headwind component on takeoff is to decrease the ground speed of
the aircraft at liftoff. An excellent illustration of this phenomenon is the “ground” speed and airspeed of a
jet airplane being launched from an aircraft carrier. The captain accelerates the ship and turns it into the
existing sea wind to get about 35 KTS of wind across the deck. Then an airplane which flies off the bow at
150 KIAS is only moving 150 – 35 = 115 KTS relative to the deck of the ship. That is, the catapult only
has to accelerate the plane to 115 KTS in the space of 200’, not 150 KTS. (Note: there have been a few
launches of jet airplanes from aircraft carriers at anchor, and these rarities are celebrated events in Naval
Aviation lore, with the pilots involved accorded significant bragging rights.)
Let VW be the wind component parallel the runway, with a positive value denoting a headwind, and a
negative value denoting a tailwind. We may conclude that
V2 = V 1 – VW
with acceleration unchanged (i.e., a1 = a2). Thus
X 2 V22 a 1  V1  VW


X1 V12 a 2  V1
2

 V
  1  W
V1


2

V  VW
V
t
V a
 , and 2  2 1  1
 1 W .
t 1 V1 a 2
V1
V1

That is:



V2 = V 1 – VW .
X2 = X1 (1 - VW / V1)2.
t2 = t1 (1 - VW / V1).
Expressed in English, these equations say that if takeoff gross weight changes from W 1 to W2:



Liftoff ground speed changes by the headwind component V W.
Takeoff roll changes as the square of (1 - VW / V1)2.
Takeoff time changes as (1 - VW / V1).
Note: the decrease/increase in takeoff roll due to headwind/tailwind also applies to landing rollouts.
Note: Let (x, y) be a point on the curve depicted in Figure 7.1. Then y / 100 = x2 if x  0.0, and y / 100 = x2 if x < 0. That is, the curve is parabolic, but this fact is obscured by different x and y scales. Also,
numbers on the x-axis are decimal fractions of the takeoff (or landing) speed, while numbers on the y-axis
are percentage changes in takeoff or landing distance, i.e., decimal fractions multiplied by 100.
Effect of Runway Slope or Gradient. The gradient G of a slope is just its rise over its run, expressed as a
decimal fraction.
Let the Cartesian x-axis lie tangent to the earth’s surface, so that the y-axis is perpendicular to the earth.
Then for a runway that has a non-zero gradient (upslope or downslope), the gradient  is just y / x, as
illustrated below.
y


W
x
W cos 
W sin  W (RG)
Rogers’s AS310 Notes, Part III: Page 4
As illustrated in the above figure, for an upslope, there is an additional weight component W sin  which
thrust must overcome, effectively decreasing thrust (the accelerating force) on takeoff. (If y is negative,
the runway has a downslope, and thrust is increased by W sin ).
Since the sin   tan  for small , we may write sin   tan  = y / x = RG, where RG is runway
gradient, so the additional force to be overcome is just W sin   W tan  = W (y / x) =W (RG). That
is, a runway gradient changes effective takeoff thrust of an aircraft by W (RG), where W is takeoff gross
weight. RG must be expressed as a decimal fraction, as is conventional. A positive value for RG denotes
an upslope, and a negative value indicates a downslope. If the runway gradient is positive (uphill),
effective thrust is decreased by W (RG); otherwise (downhill or negative gradient) effective thrust is
increased by W (RG).
Let RT/W be the thrust to weight ratio for takeoff thrust. For example, if an airplane weighs 20,000# and
has 9,000# takeoff thrust, RT/W = 9,000 / 20000 = 0.45. RT/W for high performance jet fighters often
approaches 0.75, while RT/W for an airliner might be well below 0.5. Of course, W RT/W gives takeoff
thrust in pounds for an airplane at gross weight W. For example, if W = 300,000# and RT/W = 0.20, then
takeoff thrust is just W RT/W = 300,000# (0.20) = 60,000#.
Since takeoff thrust is W RT/W, a runway gradient of RG causes effective takeoff thrust (T R)1 = W RT/W to
become (TR)2 = W RT/W - W (RG) = W (RT/W – RG), with both RT/W and RG expressed as decimal
fractions. That is,
(TR)1 / (TR)2 = W RT/W / W (RT/W – RG) = RT/W / (RT/W – RG).
Now recall the relationships that express takeoff distance and time ratios. In the case of a runway gradient,
liftoff velocity does not change since gross weight does not change. However, acceleration is changed by a
factor of (TR)1 / (TR)2, since takeoff thrust TR = F = (W/g) a, with W/g constant. That is, V 2 = V1, W2 = W1,
and a1 /a2 = (TR)1 / (TR)2 = RT/W / (RT/W – RG). Thus:
RT/W
RT/W
RT/W
RT/W
X 2 V22 a 1 V12
t
V a
V
 2
 2

, and 2  2 1  2

X1 V1 a 2 V1 R T / W  RG  R T / W  RG 
t 1 V1 a 2 V1 R T / W  RG  R T / W  RG 
To sum up, for runway gradient RG expressed as a decimal fraction (with a negative RG meaning a
downslope):



V2 = V1.
X2 = X1 [RT/W / (RT/W – RG)].
t2 = t1 [RT/W / (RT/W – RG)].
Expressed in English, these equations say that for runway gradient RG and thrust to weight ratio RT/W:


Liftoff speed remains unchanged.
Takeoff roll and takeoff time change proportional to the ratio RT/W / (RT/W – RG).
Important note: runway slope affects takeoff distance significantly more in an airplane with low thrustweigh ratio (such as an airliner) than in an airplane with high thrust-weight ratio (such as a jet fighter taking
off with combat thrust.) This is because the ratio RT/W / (RT/W – RG), for fixed RG, becomes larger as RT/W
becomes smaller.
Rogers’s AS310 Notes, Part III: Page 5
Summary of Theoretical Effects of Gross Weight, Elevation, Temperature, Wind, and Runway Slope
Changes. The foregoing results are summarized in the following table. Remember that the results for
elevation and temperature changes apply to jets and normally aspirated props, but not to supercharged
props. Also, neither one of these two results takes into account the very significant change in jet engine
thrust as temperature and/or air density change. As a result, these two equations do not predict takeoff
parameter changes as accurately as the other three.
Gross Weight:
W1  W2
Density Ratio:
1  2
Temperature:
TA1  TA2
Headwind:
VW
R/W Grad: RG &
T-W Ratio: RT/W
Liftoff (Ground) Speed
Takeoff Roll
Takeoff Time
V2 = V1  (W2 / W1)
X2 = X1 (W2 / W1)2
t2 = t1 (W2 / W1)3/2
V2 = V1  (1 / 2)
X2 = X1 (1 / 2)2
t2 = t1 (1 / 2)3/2
V2 = V1  (TA2 / TA1)
X2 = X1 (TA2 / TA1)2
t2 = t1 (TA2 / TA1)3/2
V2 = V 1 – VW
X2 = X1 (1 - VW / V1)2
t2 = t1 (1 - VW / V1)
V2 = V 1
X2 = X1 [RT/W / (RT/W – RG)]
t2 = t1 [RT/W / (RT/W – RG)]
Takeoff performance “rules of thumb” may be adduced from the above equations.. It is easy to verify their
validity from the equations. [I have put hints in brackets to help you see how to do this.]

A 21% increase in gross weight results in a 10% increase in liftoff speed [1.1 = 1.21]

A 10% increase in gross weight gives
1. a 5% increase in takeoff speed [1.1  1.05]
2. a 21% increase in takeoff distance [(1.1)2 = 1.21]
3. a 15% increase in takeoff time [(1.1)1.5  1.15]

A headwind of 10% of liftoff speed (e.g. 15 kts for 150 kt liftoff) gives
1. a 19% reduction in takeoff distance [(1 - .1)2 = 0.81]
2. a 10% reduction in takeoff time [ (1 – 0.1) = 0.9]
3. a 10% reduction in liftoff ground speed [obvious]

A tailwind of 10% of liftoff speed (e.g. 15 kts for 150 kt liftoff) gives
1. a 21% increase in takeoff distance [(1 + .1) 2 = 1.21]
2. a 10% increase in takeoff time [ (1 + 0.1) = 1.10]
3. a 10% increase in liftoff ground speed [obvious]

Shifting from a 10% headwind to a 10% tailwind (as above) increases
1. takeoff distance by about 40% [19 + 21 = 40]
2. takeoff time and liftoff ground speed by 20% [10 + 10 = 20]
Factors Ignored by Foregoing Ratio Estimations. Several important factors are not taken into
consideration by the theoretical approach above, which assumes constant acceleration on takeoff:
1.
2.
3.
4.
5.
6.
The net accelerating force (Thrust – Drag– Friction) is not constant.
Thrust drops during the runway roll for a jet engine because the air velocity at the engine
intake increases faster than at the engine exhaust point.
Parasite drag increases as a function of V2.
After rotation, induced drag increases due to increased AOA.
As lift develops, normal force on tires decreases, decreasing friction.
As a consequence of 1-5 above, takeoff acceleration is not constant, although we assumed it is
constant.
Rogers’s AS310 Notes, Part III: Page 6
Figures 7.3 and graphs typical takeoff thrust, drag, friction, and net acceleration forces vs. airspeed for a
B767. Figure 7.4 uses the net acceleration force of Figure 7.3 to graph typical B767 takeoff acceleration
vs. airspeed.
Figure 7.3. Changes to Thrust, Drag, and Friction Forces during B767 Takeoff Roll
Figure 7.4. B767 Takeoff Acceleration Profile
Inaccuracies occur when one assumes constant acceleration during takeoff roll computation. In our
equations, these inaccuracies are smaller because ratios are used to estimate changes in takeoff time,
distance, and speed as factors such as gross weight, density, temperature, and pressure change.
Rogers’s AS310 Notes, Part III: Page 7
2. Example Problems
Weight Change: An airliner at 200,000# gross takes 32 seconds and 4000’ to get airborne at 140 KTAS.
At 300,000# gross with other conditions unchanged, find takeoff time, speed, and distance.
t2 = t1 (W2 / W1)1.5 = 32 (300,000 / 200,000)3/2 = 32 (1.5)1.5 = 58.78775382 sec
V2 = V1  (W2 / W1) = 140  (300,000 / 200,000) = 140 1.5 = 171 KTAS
X2 = X1 (W2 / W1)2 = 4000 (300,000 / 200,000)2 = 4000 (1.5)2 = 9000.0000000 feet
Elevation Change. An airliner at SL on a standard day takes 32 seconds and 4000’ to get airborne at 140
KTAS. At 7000’ elevation with other conditions unchanged, find takeoff time, speed, and distance.
7000 = 0.81064
t2 = t1 (σ1 / σ 2)1.5 = 32 (1.0 / 0.81064)1.5 = 43.84377434 sec
V2 = V1  (σ1 / σ 2) = 140 1.0 / 0.81064) = 155.4941378 KIAS
X2 = X1 (σ1 / σ 2)2 = 4000 (1.0 / 0.81064)2 = 6087.008832 feet
Temperature Change. A jet fighter at SL takes 30 seconds and 4100’ to get airborne at 150 KTAS on a
day when the temperature is 0o C. If the temperature increases to 40o C with other conditions unchanged,
find takeoff time, speed, and distance.
TA2 = (40 + 273) = 313; TA1 = (0 + 273)
t2 = t1 (TA2 / TA1)1.5 = 30 (313 / 273)1.5 = 36.82932768 sec
V2 = V1  (TA2 / TA1) = 150 313 / 273) = 160.6135215w KIAS
X2 = X1 TA2 / TA12)2 = 4100 (313 / 273)2 = 5389.844633 feet
Wind Change. An airliner under no wind conditions takes 32 seconds and 4000’ to get airborne at 140
KTAS. Then with 30 KT headwind and other conditions unchanged, find takeoff time, speed, and distance.
t2 = t1 (1 – VW/V1) = 32 (1 – 30/140) = 25.14285714 sec
V2 = V1 - VW) = 140 - 30 = 110 KTAS
X2 = X1 (1 – Vw / V1)2 = 4000 (1 – 30/140)2 = 2469.38755 feet
If there is 25 KTS of tailwind, then takeoff time, ground speed and distance are
t2 = t1 (1 – VW/V1) = 32 (1 – (-25)/140) = 37.71428573 sec
V2 = V1 - VW) = 140 - (-25) = 165 KTAS
X2 = X1 (1 – Vw / V1)2 = 4000 (1 – (-25)/140)2 = 5556.122452 feet
Note that the liftoff speed IAS is not affected by headwind or tailwind; only the ground speed is changed.
Sometimes a chart (or table) is used to determine the percent change in takeoff or landing distances for a
given headwind or tailwind. An example of such a chart is given in Figure 7.1.
Rogers’s AS310 Notes, Part III: Page 8
Figure 7.1. Effect of Headwind / Tailwind Components on Takeoff and Landing Distance.
Previous Wind Change Problem Solved Graphically. An airliner under no wind conditions takes 32
seconds and 4000’ to get airborne at 140 KTAS. Then with 30 KTS headwind and other conditions
unchanged, find takeoff time, distance. Also find the takeoff distance for a 25 KT tailwind.
30/140 = 0.21 (rounded) is the fractional relation of wind speed to liftoff speed. From the origin, proceed
left on the x-axis to 0.21, then down to intersect the curve. Read 38% decrease in takeoff distance on the yaxis. 4000 – 0.38 (4000) = 2480 feet. This compares to 2469 feet computed by the equation.
-25/140 = -18% (rounded).is the fractional relation of wind speed to liftoff speed. From the origin, proceed
right on the x-axis to 0.18, then up to intersect the curve. Read 39% increase in the takeoff distance on the
y-axis. 1.39 (4000) = 5560 feet. This compares to 5556 feet computed by the equation.
Rogers’s AS310 Notes, Part III: Page 9
Runway Slope. A 300,000# airliner with 90,000# takeoff thrust takes 32 seconds and 4000’ to get airborne
at 140 KTAS on a level runway. With other conditions unchanged, find takeoff time and distance with a
runway upslope of 2% and a runway downslope of 5%.
Thrust-weight ratio RT/W = 90,000/300,000 = 0.30.
With a 2% upslope, (RG = 0.02:
t2 = t1 [RT/W / (RT/W – RG)] = 32 [0.3 / (0.3 – 0.02)] = 34.28571427 sec
X2 = X1 [RT/W / (RT/W – RG)] = 4000 [0.3 / (0.3 – 0.02)] = 4285.714284 feet
Liftoff speed remains 140 KTAS.
With a 5% downslope, (RG = -0.05):
t2 = t1 [RT/W / (RT/W – RG)] = 32 [0.3 / (0.3 + 0.05))] =27.42857143 sec
X2 = X1 [RT/W / (RT/W – RG)] = 4000 [0.3 / (0.3 + 0.05)] = 3428.571428 feet
Liftoff speed remains 140 KTAS.
Rogers’s AS310 Notes, Part III: Page 10
3. Real World Takeoff Distance Example
In contrast to our theoretical models, real world empirical data is used to construct takeoff charts which
pilots (or computers) typically use to compute takeoff distance for given gross weight, temperature, density
altitude, and headwind/tailwind component.
Navy RF8 Crusader Takeoff Distance Chart. The Takeoff Distance Chart for a U.S. Navy RF8
Crusader (Photo Reconnaissance version) using military power (as opposed to combat power, or
afterburner) is given on the next page. While the F8 is an older supersonic aircraft (capable of exceeding
Mach 1.8 and still being flown off ship by the French Navy as of November 1999), the methodology used
to compute takeoff distance is typical and not outdated. To use the chart:
1.
2.
3.
4.
5.
6.
Determine runway ambient temperature and headwind (or tailwind) component, field pressure
altitude, and gross weight.
At the lower left part of the chart, locate temperature on the vertical scale, and proceed
horizontally left to intersect the appropriate curved pressure altitude line, interpolating as
required.
From this first intersection point, proceed vertically up to intersect the appropriate straight
gross weight lines in the upper left part of the chart, interpolating as required.
From this second intersection point, proceed horizontally to the right to intersect the vertical
zero wind component line in the upper right part of the chart.
From this third intersection point, proceed parallel the curved headwind/tailwind lines until
intersecting the vertical line corresponding to headwind (or tailwind) component.
From this fourth intersection point, proceed horizontally to the right to read takeoff distance.
Practice Calculations: Determine takeoff roll for 0o C, 25 kts of headwind, SL pressure altitude, and
28,000# gross. Also determine takeoff roll at the same gross weight for 40 o C, calm wind, 2000’ pressure
altitude.
The following table contains information extracted from the F8 Takeoff Chart. It answers the two
problems posed above, and also compares actual takeoff distances to theoretical takeoff distances computed
using previously derived equations. The distance “errors” using the equations are not always small,
suggesting that the model used to formulate the equations may be somewhat naïve for predicting F8
Crusader takeoff performance. This is most noticeable in density/temperature changes, where the models
do not take account of resultant, often large changes in jet thrust.
Note: Very wide variations in takeoff roll depending on takeoff conditions are reflected in the table. In
particular, changes in pressure altitude and ambient temperature cause large changes in takeoff roll. The
table figures should alert you to the fact that accurate takeoff performance calculations are crucial to flight
safety when operating jet aircraft.
Runway Conditions
28000#, 40o C, 0 kts HWind, 2000 PA
28000#, 0o C, 0 kts HWind, 0 PA
28000#, 40o C, 0 kts HWind, 0 PA
28000#, 0o C, 0 kts HWind, 2000 PA
28000#, 0o C, 25 kts HWind, 0 PA
28000#, 40o C, 25 kts HWind, 2000 PA
24000#, 0o C, 0kts HWind, 2000 PA
24000#, 0o C, 0 kts HWind, 0 PA
24000#, 0o C, 0 kts HWind, 4000 PA
Chart Roll (ft)
10500
4100
8800
4900
2850
8000
3600
2800
3900
Theoretical Takeoff Roll (ft)
% Diff
4100 (313 / 273)2 = 5389
4100 (1.0 / 0.9428)2 = 4612
4100 (1 – 25/150)2 = 2847
10500 (1 – 25/154.5)2 =7376
4900 (24,000 / 28.000)2 = 3600
4100 (24,000 / 28.000)2 = 3012
2800 (1.0 / 0.8881)2 = 3550
-38.8%
-5.3 %
0%
-7.8%
0%
+7.5 %
-9.1 %
Rogers’s AS310 Notes, Part III: Page 11
Rogers’s AS310 Notes, Part III: Page 12
4. Importance of Acceleration Check; Premature Rotation Hazard
Takeoff Acceleration Check. Our theoretical approach to determining relative takeoff time, distance, and
liftoff speed gives useful approximations. Moreover, as we have seen, available heavy aircraft performance
data allow determining takeoff parameters much more accurately using charts and graphs based on this
data.
However, one point is abundantly clear. If the aircraft is not accelerating normally, no calculated takeoff
roll or refusal speed is helpful. That is, you calculate your go / no go speed of say 105 kts to allow you to
stop on the remaining runway when rejecting a takeoff at or below that speed. However, this refusal speed
is based on the assumption that your airplane is accelerating normally. Suppose the 105 kts speed is based
on having 4000’ remaining when you initiate the abort. If your aircraft isn’t accelerating normally, you
may not reach 105 kts until there are only 3500’ of runway remaining, and if you abort at 105 kts, you’re
likely to run off the end of the runway (hopefully at low enough speed to avoid serious damage).
Figure 7.7. Distance vs. Velocity Acceleration Check
Figure 7.8. Distance vs. Time Acceleration Check
Again, heavy aircraft have performance charts to allow you to determine how fast you should be going
after a given takeoff roll distance. However, such calculations can be done to a fairly good degree of
accuracy using the charts shown in Figure 7.7, based on data for the B767. (Figure 7.8 is a similar figure
for takeoff time as opposed to distance.) Recall that V is velocity, X distance, a acceleration, and t time.
Both these figures depict plots which are parabolic in shape, based on following observation:



VF2 = 2a and VF = at.
Thus X  VF2 and VF  t,
so X  t2.
Rogers’s AS310 Notes, Part III: Page 13
Example Calculation. Suppose rotation speed is 150 KTAS, and rotation roll and rotation time have been
determined to be 8000’ and 45 seconds respectively. Using Figures 7.7 and 7.8, determine predicted roll
and elapsed time when 75 KTAS is achieved.
75 KTAS is 75/150 = 0.5 of your takeoff speed, so from Figure 7.7 you should have covered 0.22 of your
takeoff roll, or 0.22 (8000’) = or 1760’. Note that this is less than ¼ of the total takeoff roll. From Figure
7.8, about 0.45 of the takeoff time should have elapsed, or 0.45 (45) = 20.25 seconds. That is, it takes close
to half of the rotation time but only about 1/5 of the rotation roll to get to half your rotation speed.
You can conclude that early decisions about takeoff abort are necessary. Once you get going fast, you’re
eating up runway like a roadrunner. This implies that unless a runway is extraordinarily long, you must
make an early takeoff commitment in term of runway behind you. Figures 7.7 and 7.8 tell you that when
you have used up half your takeoff roll, you’ve achieved about 73% (almost ¾) of your liftoff velocity and
used up about 70% of your takeoff time. Things happen very rapidly in the last half of the takeoff roll, and
there is no room for indecision during a time when an incorrect response to an emergency can lead to
quick and certain disaster.
Early Rotation Hazard. From Figure 7.4, we see that drag (it’s induced drag) increases significantly once
takeoff rotation starts. Thus early rotation adds additional drag to an aircraft, lengthening takeoff roll.
Another (and contrary hazard) is that you may get airborne prematurely, which can lead to serious
problems. First of all, you’re flying in ground effect, and in some airplanes a very high AOA creates so
much drag that you can’t fly through the high drag region to the front side of the thrust curve. This can be
very hairy if there are obstacles off the end of the runway. Second, you are flying near the stall speed, so
control may be difficult.
Exemplum. I flew in the reserves with a former Blue Angel Hal who was #5 for the Blues when they were
still operating Grumman F11 Tigers. At that time at least, #5 and #6 did individual high performance
takeoffs during air shows. At Andrews AFB during a show, Hal hit a bump in the active runway just at
rotation speed, got airborne prematurely (with the gear coming up), then settled back on the runway and
skidded to a stop on the remaining runway in front of a very surprised crowd. Fortunately, the aircraft
remained on the hard surface, there was no fire, and no one got hurt. But the pilot was severely
embarrassed, and with a little less luck, he could also have been severely dead. By the way, I also know
another Navy pilot Pete who did the same thing in an F8, and he was an Instructor Pilot in the F8 RAG
(Replacement Air Group), a squadron that transitioned Naval Aviators into the Crusader. Hal and Pete
were two of the Navy’s best. Moral: it’s obvious that even the best of us can make foolish mistakes, so
strive to be well-informed and diligent about safety if you want to have a long, happy flying career
unmarred by mishaps.
Rogers’s AS310 Notes, Part III: Page 14
LARGE COMMERCIAL AIRCRAFT TAKEOFF
Rules and Regulations

takeoff anomaly – an undesirable event which occurs during takeoff; e.g., engine failure, tire or
wheel problem, cockpit warning indication, bird strike, &c. After a takeoff anomaly, a decision to
continue or abort the takeoff must be made.

VMC – minimum control speed due to asymmetrical thrust with one engine inoperative. This
speed is subdivided into:
VMCG – minimum control speed during takeoff ground roll with the nose wheel still on the ground.
VMCA – minimum control speed in the air or on the ground with the nose wheel off the ground
after rotation for takeoff.
1.
2.

all engine minimum unstuck speed VMU – slowest airspeed where the airplane can be forced off
the ground with all engines operating. At this speed, the airplane will fly in ground effect but stall
out of ground effect and the settle back toward the ground.

engine out minimum unstuck speed Vmu – slowest airspeed where the airplane can be forced off
the ground with one engine inoperative. Observations immediately above apply.

VXSE – best angle of climb airspeed with one engine inoperative. 180 kts is typical for a large
swept wing jet transport airplane.

VYSE – best rate of climb airspeed with one engine inoperative. 200 kts is not atypical for a large
swept wing jet transport airplane.

climb gradient – altitude gain divided by horizontal distance covered expressed as a percent. A
climb angle of 45o corresponds to a 100% climb gradient. If it takes 4000’ along the ground to
gain 50’ of altitude, the climb gradients is (50 / 4000) 100 = 1.25%.

adequate climb capability – capability to achieve a specified critical engine out climb gradient
depending on the total number of engines on the airplane. Requirements for various takeoff
segments (defined later) are given below.

takeoff safety speed V2 – the speed after takeoff that gives an adequate climb angle (adequate
climb capability) from 35’ AGL to 400’ AGL with an engine inoperative. For large swept wing
jet transport airplanes (but not for light twins), V2 is typically less than VXSE or VYSE. V2 must be
at least 1.2 VS (1.15 VS for some airplanes) for takeoff flaps setting, and at least 1.10 V MCA.

takeoff decision speed V1 – the airspeed at which a decision must have been made to abort or
continue after a takeoff anomaly, especially an engine failure. Below V 1, an abort is feasible; after
V1, takeoff must be continued unless the ability of the airplane to fly is seriously in doubt. For
safety considerations, V1  VMCG, since at and after V1, the airplane is committed to take off.

rotation speed VR –speed at which rotation for takeoff commences. VR must allow V2 airspeed
and 35’ AGL altitude to be reached by runway end if takeoff is continued after a takeoff anomaly.
For safety considerations, VR  1.10 VMU, VR  1.05 Vmu, and VR  V1 (use limit which gives the
highest VR).

target pitch angle – the desired pitch angle at liftoff.

specified rotation rate – a takeoff rotation of 3o pitch angle per second is used to attain target
pitch angle.
Rogers’s AS310 Notes, Part III: Page 15
Takeoff Segments
Dirty Configuration
Segment A
Segment B Segment C
Segment D
Clean Configuration
Segment E
Extended Runway
Figure 8.1. Takeoff Profile Segments.
Takeoff Climb Segments. As illustrated in Figure 8.1, the takeoff profile is usually divided into five
segments. For ease of discussion, we have labeled these segments A through E on the figure. Such labels
are not conventional, and are used here for convenience only. The conventional naming of these segments
is somewhat confusing (which is typical of FARs and information derived from FARs). For instance,
Segment C (the third segment sequentially) is often called Segment 2. Also the Segments C and D (the
third and fourth segments sequentially) are sometimes grouped together:

Segment A: ground roll from release of brakes to liftoff. Occurs totally on the ground.

Segment B (1st Segment): from liftoff to 35’ AGL and V2. Called the 1st segment since it is
the first airborne segment. Adequate climb capability in this segment requires
1. a 0.5% climb gradient (5’ altitude per 1000’ of horizontal distance) with 3 out of 4
engines operating.
2. a 0.3% climb gradient (3’ altitude per 1000’ of horizontal distance) with 2 out of 3
engines operating.
3. a positive climb rate with 1 out of two 2 engines operating.

Segment C (2nd Segment): from 35’ AGL to 400’ AGL. V2 is maintained during this segment,
called the 2nd segment, since it is the second airborne segment. Adequate climb capability in
this segment requires
1. a 3.0% climb gradient (30’ altitude per 1000’ of horizontal distance) with 3 out of 4
engines operating.
2. a 2.7% climb gradient (27’ altitude per 1000’ of horizontal distance) with 2 out of 3
engines operating.
3. a 2.4% climb gradient (24’ altitude per 1000’ of horizontal distance)with 1 out of
two 2 engines operating.

Segment D (Acceleration Segment; sometimes subdivided into 3 rd and 4th Segments): segment
where airplane accelerates from V2 to 1.25 Vs (clean) at 400’ AGL. The 3rd Segment ends
when flaps are retracted. The 4th segment ends when the first throttle reduction occurs.

Segment E (Final Segment; also sometimes called the 5 th Segment): clean configuration climb
from 400’ AGL to 1500’ AGL at a speed no lower than 1.25 V s. Adequate climb capability in
this segment requires:
1. a 1.7% climb gradient (17’ altitude per 1000’ of horizontal distance) with 3 out of 4
engines operating.
2. a 1.5% climb gradient (15’ altitude per 1000’ of horizontal distance) with 2 out of 3
engines operating.
3. a 1.2% climb gradient (12’ altitude per 1000’ of horizontal distance) with 1 out of 2
engines operating.
Rogers’s AS310 Notes, Part III: Page 16
Verbal Description of Flight Operation in Each Section. We will describe aircraft / flight crew behavior
during takeoff segments A – E, under the assumption that an engine failure occurs at or after V 1.

Segment A (ground roll): The aircraft is cleared onto the runway with flaps set for takeoff.
All pertinent speeds – V1, VR, and V2 in particular – are foremost in the minds of the flight
crew. After normal runup and brake release at takeoff thrust, if an engine failure or other
serious takeoff anomaly occurs before V1, an abort is initiated. The pilot not handling the
controls calls out V1 about 5 kts before the go / no go speed is reached, and calls out V R at
rotation speed. Starting at VR, the target pitch angle is achieved using the specified rotation
rate of 3o /sec. Shortly thereafter the aircraft lifts off the runway and Segment A ends. After
V1, the aircraft cannot be stopped without overrunning the end of the runway. Essentially, a
commitment to take off exists, and an abort after V1 should be attempted only when the ability
of the airplane to fly is seriously in doubt. (For example, an explosion or fire causes extensive
damage to wing, tail assembly, or control surfaces.) If the captain initiates an abort at or after
V1, he or she is essentially saying that it is safer to run off the end of the runway at high speed
than to attempt to fly the airplane. A number of serious accidents have been precipitated
when inadvisable aborts after V1 were attempted. If you have already reached V1, it’s far too
late to abort and stay on the runway. It has been shown that initiating an abort even a second
or two after V1 can cause the aircraft to overrun the runway at speeds of 70 – 100 kts.
Remember that the airplane is full of fuel, and that if the fuel tanks rupture, the chances of a
catastrophic fire are great. Also, sudden stops from high speeds due to collision with
obstacles are not very well tolerated by the human body, and the flight crew is in the cockpit
section, which ordinarily impacts off-runway obstacles first.

Segment B (1st Segment). After an engine failure, timely gear retraction will help cut down
drag and make the airplane easier to fly. However, first priority is controlling the airplane
during the asymmetrical thrust situation. Also, gear should not be retracted until it is clear
that the airplane will not settle back onto the runway. If required, firewall thrust is applied
after the engine failure. With gear coming up and a positive climb rate established, the
aircraft (presumably) crosses the upwind end of the runway at V 2 and 35’ AGL or higher.
Flaps are still down as Segment B ends over the end of the runway.

Segment C (2nd Segment). The aircraft continues climb straight-ahead at V2 to 400’ AGL, at
which point Segment C ends. Flaps are still down, and takeoff power is maintained. Landing
gear is retracted. If you get to this point and the aircraft is firmly under control, things are
looking pretty good. Most catastrophic takeoff accidents have already occurred before the
end of Segment C.

Segment D (Acceleration Segment; 3rd and 4th Segment): The aircraft accelerates at 400’ AGL
and flaps are retracted. The 3rd Segment ends. Acceleration continues to attain an airspeed at
least 1.25 VS for the clean configuration. A power reduction to max continuous thrust occurs.
The 4th Segment ends. Segment D is concluded. If you get to this point, everything is
probably going to be OK. The people in the cabin will think the Captain is a hero once the
plane is back on the ground and they get a chance to calm down and reflect a little bit on what
has happened.

Segment E (5th Segment): In the clean configuration at or above 1.25 V S, the airplane climbs
straight ahead to 1500’. Segment E ends. At this point, the flight crew can assess the existing
emergency more fully and decide on a plan of action. For engine failure, it’s obvious that an
immediate landing is desirable, but first you have to get down to max landing weight by
dumping fuel, and many pilots will want to be even lighter than that if the reduction can be
done expeditiously.
Rogers’s AS310 Notes, Part III: Page 17
Balanced Field Length
Review of Important Definitions. As before, we assume failure of a critical engine after the airplane is
committed to takeoff (V V1).

Factors affecting V2, the takeoff safety speed for adequate climb from 35’ to 400’ AGL with
asymmetrical thrust:
1. V2  1.2 VS in the takeoff configuration, to preclude inadvertent stall.
2. V2  1.1 VMCA, to preclude inadvertent loss of control.
3. Ordinarily, V2 is significantly lower than VX, which is typically in the 180-220 kts
range for jet transports. Accelerating to VX with an engine out might require that
significant time be spent at low altitude. However, V2 must be high enough to allow
adequate climb capability with a critical engine out, as previously defined.
4. It follows that the largest of {1.2 VS, 1.1 VMCA, V for adequate climb capability}
applies.

Factors affecting rotation speed VR:
1. VR  1.10 VMU (minimum unstuck speed), or VR  1.05 Vmu (engine out minimum
unstuck speed) to avoid getting airborne at a speed where the airplane probably will
not fly out of ground effect. (The presumption here is that this restriction ensures V R
 VS in the takeoff configuration.)
2. VR  1.05 VMCA, to preclude inadvertent loss of control.
3. It follows that the largest of {1.10 VMU, 1.05 Vmu, 1.05 VMCA} applies.
4. VR  V1, refusal speed, for safety reasons. Abort after rotate is a risky undertaking.

Factors affecting V1, the decision or go / no-go speed:
1. V1  VR, as explained above.
2. V1  VMCG, to avoid loss of control while still on the runway.
3. V1 must be fast enough to allow reaching 35’ AGL and V2 at or before the end of the
runway. This allows avoiding ground obstacles.
4. V1 must be slow enough to allow stopping the airplane on the remaining runway if
an abort is initiated.
The foregoing restrictions are summarized in the following table:
Speed
V2
VR
V1
Restrictions
max (1.2 VS, 1.1 VMCA, Vadequate climb)
max (1.10 VMU, 1.05 Vmu, 1.05VMCA); VR  V1
V1  VR; V1  1.05 VMCG; V1 allows climb to 35’
AGL and / or stopping on remaining runway.
Accelerate-Go and Accelerate-Stop Distances: The following are FAR definitions.

accelerate-go distance – distance an airplane uses to accelerate to V1, experience a critical
engine failure, then continue accelerating, lift off, and achieve an altitude of 35’ AGL.

accelerate-stop distance – distance an airplane uses to accelerate to V1, then decelerate to a
stop using only brakes and spoilers (Assumes an engine has failed, making reverse thrust
unusable or inadvisable: reverse thrust is permitted on a wet runway in some cases).
The figure shown below (a recreation of Figure 9.1 in the text) plots accelerate-go and accelerate-stop
distances for values of V1 between 0 and 150 kts. Accelerate-stop distance increases as V1 increases, since
more runway is used in the accelerate phase, and the decelerate phase begins from a higher speed.
Accelerate-go distance decreases as V1 increases, since the engine failure occurs later in the takeoff roll,
hence the airplane is subject to full power for a greater portion of the takeoff.
Rogers’s AS310 Notes, Part III: Page 18
14
Distance in Feet / 1000
12
accelerate-stop
10
8
6
4
accelerate-go
2
0
0
50
100
Decision Speed V1 (KIAS)
150
Figure 9.1 (Redrawn). Accelerate-Stop and Accelerate-Go Distance vs Decision Speed.
We will discuss shortly the effect of gross weight, density altitude, and configuration changes on
accelerate-stop and accelerate-go distances. Other factors which can affect these distances include runway
slope, runway conditions, and reduced thrust settings used in thrust derated takeoffs.
Balanced Field Length. Balanced field length is the runway length where, for a given gross weight,
elevation, and takeoff configuration, accelerate-stop distance and accelerate-go distance are the same.
Since takeoff from a short runway requires optimal performance, we assume takeoff flaps are set to give
such performance. Any change from optimal flap setting for existing conditions will increase balanced
field length and V1. The graph is based on existing conditions (gross weight, temperature, wind, &c.).
In Figure 9.1, balanced field length is 6000’, and corresponds to a go / no-go speed V1 of about 130-135
KIAS. For this particular aircraft on a 6000’ runway at existing ambient conditions:
1.
2.
3.
4.
if an engine failure occurs prior to V1, the aircraft will have adequate runway remaining to
stop when an abort is initiated.
If an engine failure occurs at or above V1, the aircraft will achieve 35’AGL by the end of the
runway if the takeoff is continued.
if an abort is initiated after V1, the aircraft will overrun the runway.
if an engine failure occurs prior to V1 and takeoff is continued, the aircraft will not achieve
35’ AGL by the end of the runway. (In fact, it might not get airborne at all, if the engine
failure occurred at a very low speed!).
It is easy to draw three important conclusions from Figure 9.1 and the above observations:
1.
An airplane should never attempt to depart from a runway shorter than the balanced field
length for its particular gross weight, elevation, and takeoff configuration, since
 a decision to abort just below V1 will result in runway overrun.
 a decision to continue just above V1 will result in achieving less than 35’ AGL by the
end of the runway.
2.
If V1 is changed from the V1 corresponding to balanced field length, the runway length to
depart safely increases, since
 when V1 decreases, accelerate-go distance increases, and takeoff commitment occurs
at V1.
 When V1 increases, accelerate-stop distance increases, and a commitment to abort
exists below V1.
3.
The balanced field length concept ordinarily should be used to determine decision speed V1.
Rogers’s AS310 Notes, Part III: Page 19
Effect on Balanced Field Length of Changes in Gross Weight, Density Altitude, and Runway Slope
The table below recapitulates earlier results on takeoff speeds and distances.
Gross Weight:
W1  W2
Density Ratio:
1  2
R/W Grad: RG &
T-W Ratio: RT/W
Liftoff (Gnd) Speed
Takeoff Roll
Takeoff Time
V2 = V1  (W2 / W1)
X2 = X1 (W2 / W1)2
t2 = t1 (W2 / W1)3/2
V2 = V1  (1 / 2)
X2 = X1 (1 / 2)2
t2 = t1 (1 / 2)3/2
V2 = V 1
X2 = X1 [RT/W / (RT/W – RG)]
t2 = t1 [RT/W / (RT/W – RG)]
From the table, we can immediately conclude that increases in gross weight or takeoff elevation cause an
increase in both accelerate-stop and accelerate go distance. As a consequence, balanced field V 1 also
increases.



accelerate-stop distance increases because a higher TAS must be achieved to takeoff, because
takeoff acceleration decreases and takeoff distance increases, and because stopping from a
higher velocity requires more runway.
accelerate-go distance increases because a higher TAS must be achieved to takeoff, because
takeoff acceleration decreases and takeoff distance increases, and because reaching V 2 and
35’ AGL takes a longer distance due to decreased acceleration.
balanced field V1 increases because both accelerate-go and accelerate-stop distances increase.
VR and V2 also increase due to increases in TAS proportional to  (W2 / W1) or  (1 / 2).
These ideas are reflected in the figure shown below. Balanced field V 2 has increased something like 8-10
KIAS, and balanced field length has increased from 6000’ to about 7700’. Since IAS to takeoff has
increased, VR will also increase.
14
Distance in Feet / 1000
12
accelerate-stop
10
8
6
4
accelerate-go
2
0
0
50
100
Decision Speed V1 (KIAS)
150
The table at the top of the page also reflects the fact that runway upslope slope reduces effective takeoff
thrust without changing liftoff velocity. Thus V2 also remain constant. However, accelerate-go distance
will increase because it takes longer to reach V1, VR, and V2 and 35’ AGL. Predicting the effect on
accelerate-stop distance is more problematic, because after engine failure an upslope actually decreases
stop distance somewhat. On the other hand, it takes longer to reach the stop point with an upslope. The
overall effect of runway slope is to increase balanced field length and V 1. VR theoretically remains
constant, though some carriers increase speed slightly to compensate for reduced acceleration after rotation
due to increased induced drag.
Rogers’s AS310 Notes, Part III: Page 20
Effect of Reduced Thrust on Balanced Field Length and V1. Derated (reduced thrust) takeoffs where
feasible are routinely used by air carriers to prolong engine life. It is straightforward to see that reducing
thrust increases balanced field length and V1. Reducing thrust


increases takeoff distance and the distance required after liftoff to reach V 2 and 35’ AGL, thus
increasing accelerate-go.
ncreases distance required to reach V1 (but not to stop from V1), thus increasing accelerate-stop
distance.
Derated takeoffs are possible only when actual runway length significantly exceeds balanced field length
for full takeoff thrust.
Effect of Runway Conditions on Balanced Field Length and V1.

slippery runway – a slippery runway is one where poor braking action (rain, freezing rain, very
light ice or packed snow) increases accelerate-stop distance but not accelerate-go distance. An
increase in balanced field length will occur as a result. V1 must be decreased to allow a greater
abort rollout. VR and V2 remain unchanged.

cluttered runway – a cluttered runway is one where precipitation on the runway increases
accelerate-go distance but not accelerate-stop distance. Balanced field length will increase, as will
V1, because it takes longer to achieve a ground speed compatible with reaching V 2 and 35’ AGL
by the end of the runway. This definition is pretty much academic. Most cluttered runways are
also slippery. Such a runway is called a “slippery-cluttered” runway.
Summary of Changes to Balanced Field Length. The following graph summarizes effect on balanced
field length and V1 of weight , elevation, and runway slope increases; and of slippery/cluttered runways.
Note that all increases increase balanced field length, and that all changes except slippery runway increase
V1.
distance
stop wt, el, derate
upslope, slippery,
stop dry
Slip/clut
Clutter
slippery
dry
go wt, el, derate
upslope, cluttered
true airspeed
Slippery
Dry
Slip/clut
clutter
go dry
Rogers’s AS310 Notes, Part III: Page 21
Effect of Stopway on Accelerate-Stop Distance. A stopway is a paved runway extension, at least as wide
as the runway itself, able to support the weight of an airplane running onto it, as for example during an
aborted takeoff. Since it is not used for landing, a stopway need not be as strong as the runway itself, hence
is cheaper to construct. Of course, obstructions are prohibited in a stopway. Figure 9.14 depicts a typical
stopway.
Figure 9.14. A Typical Stopway.
Stopway length may be added to runway length in calclulating accelerate-stop distance and V1. Quite
obviously, the presence of a stopway will enable V1 to be increased beyond what it would be for runway
length alone, i.e., beyond balanced field length V1. Figure 9.15 illustrates this idea.
Figure 9.15. Accelerate-Stop Distance Including a Stopway.
Effect of Clearway on Accelerate-Go Distance. A clearway is an unpaved unobstructed area at the end
of the runway which is under control of the airport. It must extend at least 250’ to either side of the
centerline, and must have a gradient no larger than 1.25%. There is no requirement that a clearway be
paved. Threshold lights no higher than 26 inches are the only objects which may be located in a clearway.
Figure 9.16 depicts a typical clearway. Note that nothing prohibits a paved clearway with adequate load
bearing capability from functioning as a stopway.
Rogers’s AS310 Notes, Part III: Page 22
Figure 9.16. A Typical Clearway.
In calculating accelerate-go distance, up to one-half of the distance from liftoff to 35’ AGL may be over a
clearway. The presence of a clearway will increase an airplanes maximum allowable takeoff gross weight
over what it would be if the clearway did not exist. Figure 9.17 illustrates this idea.
Figure 9.17. Accelerate-Go Distance Including a Clearway.
Effect of Stopway / Clearway on Balanced Field. If a clearway is used to extend accelerate-go distance,
or a stopway is used to extend accelerate-stop distance, then the airplane is not taking off from a balanced
field.
Rogers’s AS310 Notes, Part III: Page 23
Some Important Additional Definitions. The following definitions address additional FAR restrictions
on allowable minimum runway length for takeoff. No airplane may attempt a takeoff on a runway that is
shorter than FAR Takeoff Field Length, as defined below. All definitions are for ambient conditions; i.e.,
different conditions lead to different absolute lengths in feet when applying the following definitions.



All-Engine Takeoff Distance – the distance from the start of takeoff roll to V2 and 35’ AGL
with all engines operating.
All-Engine Takeoff Field Length – 115% of all-engine takeoff distance. (See Figure 9.18)
FAR Takeoff Field Length – the larger of
1. Balanced Field Length; or
2. All-Engine Takeoff Field Length.
Note that FAR Takeoff Field Length can be limited by takeoff roll distance or by minimum climb gradient
restrictions. That is, an airplane must be capable of getting airborne in a distance that allows significant
runway still in front of it. Once airborne, it must be capable of meeting all FAR climb restrictions for
normal flight and for flight with an engine out. In essence, the airplane can be takeoff roll limited or climb
limited. This distinction is discussed further in the next section.
Figure 9.18. All Engine Takeoff Field Length
Rogers’s AS310 Notes, Part III: Page 24
B767 ALLOWABLE GROSS TAKEOFF WEIGHT, V1, V2, AND VR
Note that the calculations discussed in Chapter 13 are for the B737, and should be ignored. We will
explain how to determine B767 maximum allowable takeoff gross weight at full takeoff thrust, and the
corresponding V1, VR, and V2. (Thrust derated takeoffs are not discussed.) The procedure is conceptually
simple but somewhat elaborate in the details:
1.
2.
Determine maximum takeoff gross using various Takeoff Performance Charts.
Using maximum takeoff gross, find V1, VR, and V2 from the Takeoff Speeds Chart.
Factors Which Influence Allowable Takeoff Gross. Takeoff performance charts for the B767 allow
determining different potential maximum allowable takeoff gross weights for the active runway, as follows:






Takeoff Performance Field Limit—maximum gross takeoff weight which allows the
airplane to comply with FAR Takeoff Field Length, which is the larger of balanced field
length and all engine takeoff field length (115% of all engine takeoff distance).
Takeoff Performance Obstacle Limit—maximum gross weight which allows the airplane to
clear all obstacles by a minimum of 35’ vertically, assuming that the critical engine has failed.
Runway Contamination—slush or standing water, when present, will affect acceleration and
stop distances and hence decrease both the Field Limit and the Obstacle Limit gross weights.
Takeoff Performance Climb Limit—maximum gross weight which allows the airplane to
meet all FAR climb gradient requirements.
Takeoff Performance Tire Speed Limit—maximum gross weight which assures the
airplane’s tires can withstand centripetal stress forces that develop during the takeoff roll. As
weight increases, VLOF increases, placing more stress on the tires during takeoff roll. Tires are
usually rated at 210 or 225 mph, and can sometime limit allowable takeoff gross weight.
Takeoff Performance Brake Energy Limit—a maximum brake energy speed VMBE assures
that the airplane’s brake assemblies can absorb and dissipate heat energy created if an abort is
executed. As gross weight and takeoff/abort speeds increase, brake assembly stress increases,
creating a potential fire hazard due to overheated brakes. Thus V1 must not exceed VMBE.
The allowable takeoff gross weight is just the smallest of the Field Limit Gross, Obstacle Limit Gross,
Climb Limit Gross, and Tire Speed Limit Gross. Once computed, the figure is used to determine V1, VR,
and V2. Then, if the computed V1 exceeds VMBE, the allowable takeoff gross must be reduced, and V1, VR,
and V2 for the new gross weight must be recomputed.
Algorithm for Finding Max Allowable Takeoff Gross Weight and Corresponding V1, VR, and V2.
1.
2.
3.
Find the Field Limit Gross Weight from the Takeoff Performance Field Limit Chart.
Find the Obstacle Limit Gross Weight from the Takeoff Performance Obstacle Limit Chart.
If slush or standing water are contaminating the runway, use the Field Limit and Obstacle
Limit Reduction Chart to reduce the Field Limit and Obstacle Limit Gross Weights.
4. Find the Climb Limit Weight from the Takeoff Performance Climb Limit Chart.
5. Find the Tire Speed Limit Weight from the Takeoff Performance Tire Speed Limit Chart.
6. Find the Max Brake Release Weight, which is the minimum of the Field Limit Weight, the
Obstacle Limit Weight, the Climb Limit Weight, and the Tire Speed Limit Weight.
7. Determine preliminary V1, VR, and V2 from the Takeoff Speeds Chart using Max Brake
Release Weight computed in step 6.
8. If the Max Brake Release Weight is the Climb Limit Weight, the airplane is climb limited. In
that case, use the Improved Takeoff Performance Climb Limit Chart to increase the Max
Brake Release Weight. Preliminary V1, VR, and V2 values will also increase.
9. Use the Brake Energy Limit Chart to determine if preliminary V 1 exceeds VMBE. If it does,
adjust the Max Brake Release Weight downward accordingly. V1, VR, and V2 also decrease.
10. If step 9 lowered the Brake Release Weight, re-enter the Takeoff Speeds Chart with the new
gross weight to determine final V1, VR, and V2. Adjust speeds if aircraft is climb limited.
Rogers’s AS310 Notes, Part III: Page 25
B767 Takeoff Charts may be found in an appendix to Part II of the class text. The title of the appendix is
“Boeing 767 Operations Manual.” Most required charts are reproduced in the class notes.
Determining Takeoff Performance Field Limit (Step 1). This gross weight is determined from the
Takeoff Performance Field Limit Chart. The weight, read on the right vertical scale of the chart,
corresponds to the intersection of two distinct trace lines. This weight must then be incremented if bleed
packs will be off for takeoff, and decremented if engine and wing anti-icing systems will be utilized.
1.
2.
3.
4.
5.
Construct the first trace line:
a. Enter the chart on the lower right horizontal scale with the field (runway) length.
b. Proceed vertically upward to the first reference line.
c. Follow the slanted guide lines to the runway slope on the right vertical scale.
d. Proceed vertically upward to the second reference line.
e. Follow the slanted guide lines to the headwind component on the left vertical scale.
f. Proceed vertically upward to the third reference line.
g. Follow the slanted guide lines to the flap position on the right vertical scale.
h. Proceed vertically upward to the top of the chart.
Construct the second trace line to its intersection with the first trace line:
a. Enter the chart on the lower left horizontal scale with the runway temperature.
b. Proceed vertically upward to the pressure altitude.
c. Proceed horizontally to the right to the vertical reference line.
d. Follow the slanted guide lines to intersect the first trace line.
At the intersection of the second trace line with the first trace line, proceed horizontally to
read the allowable field limit gross weight on the right vertical scale.
If bleed packs will be off for takeoff, add 1100# to the allowable field limit gross weight.
(See note lower left of chart)
If engine and wing anti-ice systems will be on, subtract 3090# from the allowable field limit
gross weight. (See table at lower left of chart.)
Determining Obstacle Performance Limit (Step 2). This gross weight is determined from the Takeoff
Performance Obstacle Limit Chart. Four trace lines must be constructed. Be sure to choose the chart
corresponding to planned takeoff flaps setting. (Only the Flaps-5 chart is included in the notes. The class
text contains both a Flaps-5 and Flaps-15 chart.)
1.
2.
3.
4.
5.
Construct the first trace line:
a. Enter the chart on the lower left horizontal scale with the runway temperature.
b. Follow the slanted pressure altitude lines to the pressure altitude on the lower left
vertical scale.
c. Proceed vertically upward to intersect the flap setting slanted line.
d. Proceed horizontally to the right margin of the chart.
Construct the second trace line to its intersection with the first trace line.
a. Enter the chart on the lower right horizontal scale with the distance to the obstacle.
b. Proceed vertically upward to the horizontal reference line.
c. Follow the slanted lines to an intersection with the first trace line.
Construct the third trace line. From the intersection of the first and second trace lines,
proceed vertically upward to the top of the chart.
Construct the fourth trace line.
a. Enter the chart on the upper left vertical scale with the obstacle height.
b. Proceed horizontally to the right to the vertical reference line.
c. Follow the slanted wind reference lines to the headwind or tailwind component.
d. Proceed vertically to the right of the chart.
At the intersection of the third and fourth trace lines, read obstacle limit gross weight using
the slanted weight lines.
Rogers’s AS310 Notes, Part III: Page 26
Adjusting Field and Obstacle Performance Limit Gross Weights for Runway Contaminants (Step 3).
A slippery runway decreases braking effectiveness, decreasing V 1 and increasing balanced field length. A
cluttered runway decreases acceleration, increasing both V 1 and balanced field length. Use the
Slush/Standing Water Takeoff Chart to decrease allowable field and obstacle performance gross weights.
1.
2.
3.
4.
Enter the chart with the calculated gross weight, pressure altitude, and depth of slush/standing
water.
Read the weight reduction in the appropriate column.
Three levels of linear interpolation will be required to obtain the best safe gross weight. (If
interpolation is not used, always round up to the higher value to achieve a conservative
takeoff gross weight figure. This figure will be less than the “best” gross weight.)
a. Interpolation between two gross weights.
b. Interpolation between 0.25” and 0.5” of slush/water.
c. Interpolation between two pressure altitudes
The weight computed must be subtracted from the gross weight used to enter the chart.
Determining Takeoff Performance Climb Limit (Step 4). This gross weight is determined from the
Takeoff Performance Climb Limit Chart.
1.
2.
3.
4.
5.
6.
7.
Enter the chart on the lower right horizontal scale with the runway temperature.
Proceed vertically upward to intersect the pressure altitude, using the slanted lines to
interpolate.
From the pressure altitude intersection, proceed horizontally left to intersect the vertical
reference line.
From the reference line, use the slanted lines to proceed to the flap position indicated on the
lower left horizontal scale.
From the intersection with the flap position, proceed horizontally to read the climb limit gross
weight on the left vertical scale.
If air conditioning packs will be off, increase calculated gross weight by 3100#. (See note at
lower left of chart.)
If engine and wing anti-ice will be used, decrement the calculated gross weight 3500# for
Flaps 5 takeoff or 3300# for Flaps 15 or Flaps 20 takeoff. (See box at lower left of chart.)
Determining Takeoff Performance Tire Speed Limit Step 5). This gross weight is determined from the
Takeoff Performance Tire Speed Limit Chart. The chart for 225-mph tires is given in the notes.
1.
2.
3.
4.
5.
Enter the chart on the bottom horizontal scale with the runway temperature.
Proceed vertically upward to intersect pressure altitude, using the slanted lines to interpolate.
From the pressure altitude intersection, proceed horizontally to read the flaps 5 tire speed limit
weight on the left vertical scale.
For flaps 15, increase gross weight limit by 26,500#. For flaps 20, increase by 50,300#.
(Notes at bottom of chart.)
For each knot of headwind component, increase weight limit by 2,600#. For each knot of
tailwind, decrease weight limit by 4,300#. (Note at bottom of chart.)
Determining V1, VR, and V2 (Steps 7, 10). Use the Takeoff Speeds Chart and to compute these values.
1.
2.
3.
4.
In the upper left portion of the figure, find the intersection of pressure altitude on the left
vertical scale with runway temperature on the bottom horizontal scale. This intersection falls
in one of five column reference areas of the graph: A, B, C, D, or E.
Enter the table in the flap setting row and column reference column to read V1, VR, and V2
corresponding to the previously computed maximum allowable takeoff gross weight.
Adjust V1 for wind and runway slope by referring to the small table at the upper right of the
figure. Adjustments must not increase V1 beyond VR.
If V1 falls in a shaded area, it may be less than VMCG. In that case, consult the table at the
lower left of the figure to increase V1 to VMCG.
Rogers’s AS310 Notes, Part III: Page 27
Determining Takeoff Performance Improved Climb Limit (Step 8). Allowable gross takeoff weight is
the minimum of the field limit, obstacle limit, climb limit, and tire speed limit weights. If the climb limit is
smallest, then the airplane is climb limited. A higher V2 gives a higher rate of climb rate. Use the Takeoff
Performance Improved Climb Limit Chart to increase allowable takeoff gross (V2 will also increase). Two
calculations – Field Length Limit and Tire Speed Limit – must occur. The same algorithm works for both:
Compute Field Limit Weight – Climb Limit Weight, or Tire Speed Limit Weight – Climb
Limit Weight, depending on which chart will be used.
2. Enter the chart on the lower horizontal scale with this difference.
3. Proceed vertically upward to intersect the normal climb limit weight line.
4. From the intersection, move horizontally to read gross weight improvement on the left
vertical scale.
5. From the intersection, move horizontally to read V1 increase to the right of the chart.
6. Continue right to intersect vertical reference line.
7. Follow the slanted lines to intersect vertical normal climb limit weight line.
8. From the intersection, move horizontally to read VR and V2 increase on the right vertical
scale.
9. When two climb limit increases have been calculated, add the lesser of the two to the takeoff
performance climb limit gross weight. (V1, VR, and V2 will also increase)
10. The resultant figure gives the maximum allowable gross weight for takeoff.
1.
Determining Takeoff Performance Brake Energy Limit Speed (Step 9). Use the Takeoff Performance
Brake Energy Limit Chart to assure that V1 as calculated above is not greater than the maximum allowable
brake energy limit speed VMBE. If it is greater, reduce allowable takeoff gross and recompute V 1, VR, and
V2.
1.
2.
3.
4.
5.
6.
7.
8.
9.
Enter the chart at the upper left with the pressure altitude on the left vertical scale and
allowable takeoff gross weight on the bottom horizontal scale.
Proceed vertically up from the gross weight and horizontally right from the pressure altitude
to find the intersection of these two lines.
If the intersection falls outside the shaded area, or when operating with a tailwind or using
improved climb gross weight, continue with step 4. Otherwise, V MBE  V1, and the
computation is complete.
From the intersection, proceed horizontally right to intersect the runway temperature.
From the intersection with runway temperature, proceed vertically down to intersect
calculated max takeoff gross weight.
From the intersection with gross weight, proceed horizontally to read V MBE on the right
vertical scale.
Adjust VMBE for runway slope, headwind/tailwind, or inoperative anti-skid brake feature, as
indicated in the table at the lower left of the figure.
Follow instructions at bottom of figure for normal takeoff gross weight or improved climb
takeoff gross weight to determine how much the allowable takeoff gross from step 1 must be
reduced.
Using the reduced allowable takeoff gross, determine new values for V 1, VR, and V2. If the
airplane is climb limited, use the Climb Limit Performance Chart to find revised values for
incrementing V1, VR, and V2.
Rogers’s AS310 Notes, Part III: Page 28
Example Calculation Using Algorithm on Pages 23. Suppose the following conditions exist at B767 takeoff:
Runway Length: 12000’
Runway Temperature: 32o F (0o C)
Conditions: 0.25” Standing Water
Anti-Ice: Off
Obstacle: 22000’ from the takeoff end 100’ above lowest point
Pressure Altitude: 4000’
Runway Downslope: 2%
Flap Position: Flaps 5
A/C Packs: On
Wind: 10 kt tailwind
Tires: 225 mph
1.
Takeoff Performance Field Limit: 395,000# – 5,025# = 389,975#.
Takeoff Performance Field Limit Correction for Runway Contamination: 5,025#:
Subtract 5,700# at 380,000# gross. Subtract 4,800# at 400,000# gross.
At 395,000# gross,
 395,000  380,000 
Subtract 5,700  
 5,700  4,800 = 5,700 – (0.75) (900) = 5,025#
 4000,000  380,000 
2.
Takeoff Performance Obstacle Limit: 380,000# - 5,700# = 374,300#.
Takeoff Performance Obstacle Limit Correction for Runway Contamination: 5,700#.
Subtract 5,700# at 380,000# gross.
3.
Takeoff Performance Climb Limit: 373,000#.
4.
Takeoff Performance Tire Speed Limit Weight: 445,000# - 10 (4,300)# = 402,000# (10 kt tailwind).
5.
Maximum Authorized Brake Release Weigh is 373,000#, which is the minimum of:

Final Takeoff Performance Field Limit: 389,975#.

Final Takeoff Performance Obstacle Limit: 374,300#.

Takeoff Performance Climb Limit: 373,000#.

Takeoff Performance Tire Speed Limit: 402,000#.
6.
From Takeoff Speeds Chart, at 373,000# gross and Flaps 5:

Pressure altitude / temperature category is B.

V1 = 157 kts; VR = 160 kts; V2 = 166 kts.

Slope adjustment to V1 is –3 kts, and wind adjustment is –1 kts.

Final V1 = 157 – 3 – 1 = 153 kts. This is well above VMCG of 103 kts.
7.
Airplane is climb limited, so determine Improved Takeoff Climb Performance Limits.

Field Length Limit Improvement: Field Limit Weight – Climb Limit Weight = 389,975# – 373,000# =
16,975#. Climb Weight Improvement: 5,700#. Add 4 kts to V1, and 4 kts to VR and V2.

Tire Speed Limit Improvement: Tire Limit Weight – Climb Limit Weight = 402,000# - 373,000# = 29,000#.
Climb Weight Improvement: 5,800#. Add 4 kts to V1, and 4 kts to VR and V2.
8.
Improved Takeoff Performance Climb Limit: 373,000# + 5,700# = 378,700#.



9.
Add lesser of Field Length (5,700#) and Tire Speed (5,800#) Improvements to takeoff gross.
Improved takeoff max gross is 378,700#.
Add 4 kts to V1, and 4 kts to VR, and V2: V1 = 153 + 4 =157; VR = 160 + 4 = 164; V2 = 166 + 4 = 170.
VMBE from Brake Energy Limit (BEL) Chart: 175 – 8 – 22 = 145 kts.

Decrease 8 kts for 2% downgrade.

Decrease 22 kts for 10 kt tailwind.

V1 = 157 kts and VMBE = 145 kts, so subtract 12 (800) = 9,600# from climb improved weight giving
369,100#. This exceeds actual climb improved weight ,so now apply the VMBE check to 373,000#.
10. Determine Final Takeoff Gross and Corresponding Airspeeds:

Max Takeoff Gross Weight (Climb Limit) = 373,000#. Corresponding V1 = 153, VR = 160, V2= 166.

From BEL Chart, V1 –VMBE = 7, so must subtract 7 (1,800) = 12,600# from Takeoff Gross of 373,000#.

Final Max Takeoff Gross: 373,000 – 12,600 = 360,400#.

From Takeoff Speed Chart, V1 = 154 – 3 – 1 = 150; VR = 157; V2 = 163.
The climb limit gross was increased 5,800# using improved climb performance, then reduced since the improvement
produced a V1 that exceeded VBME. We discovered that no climb improvement was possible. Finally, in fact, the
original Climb Limit Gross of 373,000# was reduced (because of VBME) to 364,000#, and V1 reduced to 150 kts.
Rogers’s AS310 Notes, Part III: Page 29
Step-by-Step Explanation of Solution to Quiz on Preceding Page
1.
Determine the uncorrected field limit gross weight from the Field Limit Chart. Use the Runway Contamination
Table to determine how much weight to subtract from the initial field limit gross. Do the subtraction to determine
the final field limit weight.
2.
Determine the uncorrected obstacle limit gross weight from the Obstacle Limit Chart. Use the Runway
Contamination Table to determine how much weight to subtract from the initial obstacle limit gross. Do the
subtraction to determine the final obstacle limit weight.
3.
Determine the climb limit weight from the Climb Limit Chart.
4.
Determine the tire limit weight from the Tire Limit Chart, being sure to correct for existing tailwind.
5.
Choose the smallest of the four weights found in steps 1-4. This weight is the climb limit weight, and is the
current proposed max gross takeoff weight.
6.
Use the V1, VR, and V2 Table to find each of these speeds for the climb limit weight determined in Step 5. Be sure
to correct V1 for existing down slope and tailwind.
7.
Since the climb limit weight is the lowest weight in step 5, use the Climb Limit Chart to determine two values: a)
how much weight can be added due to excess field length and b) how much weight can be added due to excess tire
speed capacity. Note that adding weight requires an increase in V 1, VR, and V2, and that the increases for both
weight increments can be determined from the Climb Limit Chart.
8.
Add the lower of the two weight increments to the climb limit weight, giving a new and higher proposed max
gross takeoff weight. In this case, the lower increment is the one associated with the field length weight. Increase
V1, VR, and V2 as determined in step 6 by the amount associated with the field length weight increment, as
determined in step 7. The idea here is that the increased V 2 will give FAR acceptable climb gradients at the higher
proposed max gross takeoff weight. You now have a climb improved weight (378,700#) and corresponding V1,
VR, and V2. This weight is the new proposed max gross takeoff weight.
9.
Subject the weight determined in Step 8 to the Brake Energy Limit test. You find that because of the runway
gradient and tailwind you must remove more weight (9,600#) from the aircraft than you added in step 8 (5,700#).
At this point, abandon the climb improvement attempt and revert to the proposed takeoff weight of step 5, which
is the original climb limit weight (373,000#).
10. Subject the original climb limit weight (373,000#) to the Brake Energy Limit test, just as you did for the climb
improved weight in step 8. Use the associated V1, VR, and V2 determined in step 6. You find you must remover
12,600# from the aircraft due to down slope and tailwinds, giving a final proposed max gross takeoff weight of
360,400#. Note that in step 9 you subtracted 800# / knot that V 1 exceeds VMBE, because you were preparing for a
climb improved takeoff. In this step, you subtract 1,800# / knot, since the calculation is for a normal takeoff, as
compared to a climb improved takeoff. Accept this weight (360,400#) as you max gross takeoff weight, since it is
smaller than the weight determined in step 9.
Rogers’s AS310 Notes, Part III: Page 30
B767 Takeoff Performance Field Limit Chart.
Rogers’s AS310 Notes, Part III: Page 31
B767 Flaps 5 Takeoff Performance Obstacle Limit Chart.
Rogers’s AS310 Notes, Part III: Page 32
B767 Field Limit and Obstacle Limit Weight Reduction Chart for Slush / Standing Water/
Rogers’s AS310 Notes, Part III: Page 33
B767 Takeoff Performance Climb Limit Chart.
Rogers’s AS310 Notes, Part III: Page 34
B767 Flaps-5 Takeoff Performance Tire Speed Limit Chart, 225 MPH Tires.
Rogers’s AS310 Notes, Part III: Page 35
B767 Takeoff Speeds Chart.
Rogers’s AS310 Notes, Part III: Page 36
B767 Takeoff Improved Climb Performance Chart.
Rogers’s AS310 Notes, Part III: Page 37
B767 Brake Energy Limit VMBE Chart.
Rogers’s AS310 Notes, Part III: Page 38
A REAL WORLD EXAMPLE OF TAKEOFF CALCULATIONS
Since takeoff calculations are tedious and error-prone when performed by humans, they are often
automated. When dispatch computer assistance is not available, simplified procedures are sometimes used
to save time and reduce the probability of error. We will explain takeoff calculation procedures used by
Tower Air, a budget airline company which currently operates worldwide using B747s exclusively. A
Tower B747 Captain who retired in May 1999 supplied the following information.
Overview of Tower Air Takeoff Calculations. A Tower B747 Captain taking off from a specified active
runway at a given location either performs the following activities or assures they are performed by a flight
crew member. Note that the Captain can delegate his authority but not his responsibility. If authority is
delegated and a calculation error results, the Captain is still responsible for the error.
1.
Determine the maximum allowable takeoff gross weight for the active runway and existing
conditions. As described later, this weight is found by using Airport Analysis Charts supplied
to Tower under contract with Jeppesen-Sanderson. Temperature, pressure altitude, headwind
component, runway condition (slippery, cluttered, &c.) are among the runway parameters
which affect the allowable takeoff weight. Airplane parameters include structural limit, climb
limit, and maximum engine operating temperature
2.
Using Tower/Boeing Takeoff Speed Tables and temperature, pressure altitude, and actual
gross weight, determine balanced field V1, VR, and V2. These Speed Tables exist for
maximum permissible thrust takeoffs, and for derated thrust takeoffs. If actual gross is well
below maximum allowable takeoff gross (i.e., if balanced field length is significantly shorter
than actual runway length), a derated thrust takeoff is always used to prolong engine life.
3.
The Captain is responsible for assuring that existing conditions (temperature, pressure
altitude, gross weight) at time of takeoff are compatible with the figures used earlier to
determine takeoff speed parameters.
From the above description, two facts emerge:

In essence, Tower airplanes always take off on a balanced field. If actual runway length
exceeds balanced field length for full power takeoff, thrust derating used to prolong engine
life has the effect of extending the balanced field length until it is approximately the same as
the actual runway length same (but of course never greater!).

Surprisingly, there is no acceleration check procedure, even though V 1 is not a meaningful
speed if the aircraft is not accelerating normally. (For example, if you expect to reach V1 after
rolling 40% of the runway length, and then don’t actually reach that speed until half the
runway is gone, then an abort right below V1 will cause the airplane to overrun the runway.)
To a single engine pilot, this omission seems strange. However, there appear to be several
mitigating circumstances, as follows.
1.
2.
3.
4.
Airliners have more than one engine, and if engine instruments for each engine
reflect proper thrust output, and the readings agree for all engines, there is only a
very small probability that any engine is producing abnormally low thrust.
Most heavy transport Captains have significant experience in type. Presumably,
such a seasoned individual would be able to detect abnormally slow acceleration as
the aircraft rolls down the runway. (But this is a sometimes dubious presumption, as
attested to by a number of serious but preventable pilot induced takeoff accidents.)
Engine failures on takeoff are very rare indeed, and even if an aircraft is accelerating
abnormally slowly, with all engines operating it is unlikely that it won’t get airborne
well before the end of the runway.
Many safety factors are built into the takeoff decision charts, as explained shortly.
Rogers’s AS310 Notes, Part III: Page 39
Nevertheless, it would be easy to compute acceleration check speeds/distances from the same information
used to determine V1, VR, and V2. Such data would give, for example, minimum acceptable indicated air
speeds after 1500’, 3000’, and perhaps 4000’ of takeoff roll (assuming V 1 occurs after 4000’ of roll, which
is certainly not always the case). If these minimum speeds were not achieved , the takeoff would then be
aborted. For runways lacking distance remaining markers, roll time to achieve a specified speed could be
determined.
Details of Tower’s Allowable Gross Takeoff Weight Calculations. Allowable takeoff weight is
determined by the most restrictive of several factors, grouped into two broad categories: Airplane Limits
and Runway Limits.


Airplane Limits depend on airplane characteristics as opposed to runway conditions.
1. The structural limit is determined by the strength of the airplane structure, and may
not be exceed under any circumstances.
2. The climb limit is determined by the maximum weight at which the airplane can still
comply with FAA takeoff climb gradient restrictions.
3. The maximum operating temperature limit is the FAA authorized maximum
temperature for takeoff due to engine and accessories cooling requirements. Under
no circumstances may this limit be exceeded.
Runway Limits comply with the FAA Takeoff Field Length restriction. The runway length
must be the greatest of:
1. 115% of the 4-engine takeoff distance to V2 and 35’ AGL.
2. Distance to accelerate to V1, recognize a loss of an engine at V1, retard all engines,
apply maximum breaking, raise the spoilers, and bring the aircraft to a full stop
without using reverse thrust. (But 2-engine reverse thrust is available with B747, an
added safety margin.)
3. Distance to accelerate to V1, lose an engine, and continue takeoff to V2 and 35’ AGL.
In addition, gross weight restrictions may be imposed because of tire limitations; or because of limited
ability of the wheel brake assemblies to absorb and dissipate heat incurred during an aborted takeoff.
To find allowable takeoff gross, enter the Jeppeson-Sanderson chart for the departure airport. These charts
are utilized by Tower since they take into account factors not normally known by the pilot, e.g., existence
of departure obstacles, or of stopways and clearways. As shown in the Kennedy International chart (not
supplied in these notes):
1.
2.
3.
4.
5.
6.
7.
8.
Max departure temperature is shown in the upper left portion of the chart (item 3).
If a turn following departure is required for a given runway, this fact is reflected at the top of
the column corresponding to that runway, and departure intersection, if relevant: (item 10).
Details of the turn procedure are specified on a separate page of airport information.
Each row of the chart corresponds to the temperature in column 1 (item 11: C on left, F on
right). Enter the chart with ambient runway temperature.
The figure in column 2 (first column to the right of the ambient temperature) reflects the max
allowable gross takeoff weight which allows meeting all FAA mandated climb requirements
(item 12).
The figure (item 13) in the column corresponding to departure runway and intersection
reflects the smallest of
a. runway weight
b. obstruction clearance weight.
c. tire restriction speed weight.
d. VMCG restriction weight.
If an asterisk appears after the weight in the runway column, then this weight exceeds the
climb limit weight in column 2.
Maximum allowable takeoff EPR is given in the second column from the right (item 15).
Available runway length is given at the bottom of the column corresponding to the runway,
and departure intersection, if relevant (item 16).
Rogers’s AS310 Notes, Part III: Page 40
9.
Gross weight corrections for headwind (add the correction) or tailwind (subtract the
correction) are given at the bottom of the runway columns (item 18, 19).
The allowable max takeoff weight is the lesser of the climb limit weight in column 2 of the ambient
temperature row, and the weight listed at the intersection of the temperature row and runway column.
Rogers’s AS310 Notes, Part III: Page 41