Experiment #2
Aircraft Glide and Climb Performance
Frasca 242 Pilot Training Device (Baron 58)
(Revised 2/23/07)
Objectives
To determine the:
1. Best glide speed (Vbg), best angle of climb speed (VX), and
the maximum level flight speed (VM).
2. Collect and compute, when necessary, the nine bootstrap
parameters; S, AR, P0, C, d, CD0, e, m, and b (wing area,
aspect ratio, engine brake horsepower at sea level, altitude
drop off parameter, propeller diameter, parasite drag
coefficient, Oswald’s efficiency factor, propeller polar
slope, and propeller polar intercept).
3. Compare climb and glide speeds at altitude with those
published in the Pilot’s Operating Handbook.
Instrumentation
1. Airspeed indicators; calibrated for instrument and position
errors. Be careful to note the units of the airspeed
indicators. Some aircraft dials have units of knots and
some have units of miles per hour (mph). The Frasca uses
units of knots.
2. Altimeters; calibrated for instrument and position errors.
3. Rate of climb indicator.
4. Calibrated fuel quantity gauges.
5. Outside air temperature, calibrated for instrument error
and recovery factor.
6. Stop watch.
Stabilized Flight Techniques
A. Glide Test
1. Begin at an altitude at least 500 feet above your chosen
start point, maintaining level flight reduce throttles until
the desired glide speed is attained.
2. Once the desired glide speed has been attained reduce the
throttles to idle and feather the propeller and establish a
stabilized glide using pitch attitude to set desired glide
speed. Take care to maintain airspeed within plus or minus
1 knot.
3. When stable, record data shown on the data card.
4. Recover from the glide at least 500 feet below your chosen
finish point.
B. Climb Test
5. When recovered from the glide maintain level flight at
least 500 feet below the chosen start point.
6. Adjust the throttles to achieve the desired airspeed for the
upcoming climb.
7. Once the desired airspeed is stable, apply full power with
the throttle and put the aircraft in a steady speed climb by
using pitch attitude to set climb speed. Take care to
maintain airspeed within plus or minus 1 knot.
8. When stable record data shown on test card.
9. Recover from climb 500 ft above target altitude and repeat
Glide and Climb test as needed.
C. Maximum Level Speed
10. When finished with climbs and glides, stabilize the aircraft
in level flight at the midpoint altitude for the climbs and
dives.
11. Advance the throttles to maximum power while
maintaining level flight.
12. When airspeed stabilizes record data on test card.
Performance Data Card
Aircraft:
A. Glide
Operating Empty Weight (OEW,
a/c wt - wt of fuel) _________lbf
1
2
3
4
5
6
Wf-glideWeight of fuel (lbf)
Vaim Aim Airspeed (knots)
Haim Aim Pressure Alt. top of
glide (ft) (~5500 ft)
Hi-start Pressure Alt. start of glide
(ft) (~5200 ft)
Vi-start Indicated Airspeed at start
of glide (knots)
Watch time at 5200 ft (sec)
105
110
115
120
125
130
2500
2500
2500
2500
2500
2500
Bootstrap Approach
Data Card (continued)
Aircraft:
C. Max Level Speed
WfM Weight of fuel (lbf)
HpM Pressure Alt. (ft)
TM OAT top of glide (degC) watch
units!
ViM Airspeed (knots)
Propeller RPM
Manifold Pressure (in Hg)
Tmid OAT 5000ft (degC)
Watch time at 4800 ft (sec)
Hi-end Pressure Alt. end of glide
(ft) (~4800 ft)
Vi-end Indicated Airspeed at end
of glide (knots)
B. Climb
Wi Initial weight of fuel(lbf)
Vaim Aim Airspeed (knots)
Pressure Alt. bottom of climb, ft
(~4500 ft)
Vi-start Ind. Aspd at 4800 ft (knot)
Tmid OAT 5000 ft (degC)
Vi-end Indicated Airspeed 5200 ft
(knots)
Wf Final weight of fuel (lbf)
tc Elapsed time from 4800 to
5200 ft (sec)
85
90
95
100
105
110
1500
1500
1500
1500
1500
1500
Miscellaneous data for the Beech Baron 58
n_engines=2
Number of engines, integer
Hp_per_engine=285
Horsepower per engine, Hp
(The Frasca 242 has a slightly smaller engine then the 300 hp
engine we have been studying in class)
Nominal_RPM=2700
RPM at rated engine Hp
P0 = n_engines*Hp_per_engine*550 Sea level brake
horsepower, ft-lbf/sec
n0RevPerSec = Nominal_RPM*(1/60) Sea level engine
rotation, revolutions per second
omega0=n0RevPerSec*2*pi
Sea level engine rotation,
radians per second
Known Bootstrap parameters
S = 199.2
Wing area, ft^2
B=37.833
Wing span, ft.
A = 7.1855
Aspect ratio, non-dimensional
M0= P0/omega0 Rated Mean Sea level Torque
C = 0.12
Altitude drop-off parameter, nondimensional
d = 76*(1/12)
Propeller diameter, ft
A. Glide Test – Data Reduction
1
Vi (kts) (average of
Vi-start and Vi-end)
2
Vc (kts)
3
Ve (kts)
4
VT (kts)
5
Hi-start (ft) (~5200
ft)
6
Hc-start (ft)
7
Hi-end(ft) (~4800
ft)
8
Hc-end (ft)
9
Pmid (lbf/ft2)
10 Tmid OAT (degR)
11 mid-glide(slug/ft3)
12 mid (non-dm)
13 Hc (ft)
14
Ts at Hp=5000 ft
(degR)
15 H (ft)
16 Wglide (lbs)
17
t Elapsed time of glide
from 5200 to 4800 ft (sec)
A. Glide Test Data Reduction
Wing area (S) = 199.2 ft2 Wing Aspect Ratio (A) = 7.17
Sea Level Brake Horse Power (P0) = 2*285hp
Altitude drop-off parameter (C) =0.12. Prop diam (d)=76/12 ft.
1. Indicated Airspeed (use average for glide)
2. Calibrated Airspeed (use MATLAB function
AS1Baron58.m)
3. Equivalent airspeed (use MATLAB function AS2.m)
4. True Airspeed (use MATLAB function AS3.m)
5. Indicated pressure altitude (at the start of the glide)
6. Calibrated pressure altitude (at the start of the glide) (use
MATLAB function ALTBaron58.m)
7. Indicated pressure altitude (ending value of the glide)
8. Calibrated pressure altitude (use MATLAB function
ALTBaron58.m)
9. Pmid Atmospheric pressure at the mid point of the glide
(5000 ft) (use MATLAB function atmosphere4.m)
10. Tmid Convert OAT at 5000 ft from degC to degR.
degF=degC*9/5 + 32
degR=degF + 459.67
11. Density at midpoint of glide
 midglide 
Pmid
[9]

RT mid R[10]
R=1716.55 ft^2/(sec^2degR)
12. Density ratio:mid

mid=mid/0
0=.0023769 slug/ft^3
13. Change in calibrated pressure altitude for glide: step [6] –
step [8]
14. Ts Standard temperature for pressure altitude at midpoint
of glide (5000 ft) (use MATLAB function atmosphere4.m)
T
[10]
[13]
15. True change in altitude: H  mid H c 
Ts
[14 ]
16. Aircraft weight Wglide=OEW + weight of fuel for glide
17. t= Watch time at 5200 ft - Watch time at 4800 ft (sec)

B. Glide Test Data Analysis
1.
2.
3.
Put your glide data in a data file called Baron58_GLIDE_data.txt in a
similar format to the example file at the class web site
http://roger.ecn.purdue.edu/%7Eandrisan/Courses/AAE490A_S2006/
Buffer/Climb/.
Run the MATLAB script Baron58_Step_1_Glide.m. Plot the drag
polar and determine the values of CD0, k and e using a least squares fit
to the lift coefficient and drag coefficient data.
The glide velocity that results in the longest glide distance occurs
when the angle , see Figure 1, is minimized. The best glide angle is
referred to as bg. Glide angle is given by the following equation
  sin 1

t
Figure 1
H
V t
Let G = -  to avoid having to plot negative angles
4.
Plot the angle G versus true airspeed like in Figure 2.
5.
As demonstrated on Figure 2, find the minimum value of the angle G.
Gbg is the negative value of the best glide angle,  . The true airspeed
corresponding to this angle is the best glide speed Vbg and the weight
of the aircraft at that flight condition is the best glide weight Wbg. You
will need to convert Vbg from knots to ft/sec using
Vbg(ft/sec) = Vbg(knots)*1.688
Compare the glide performance with data published in the Pilot’s
Operating Handbook. [Glide: propellers feathered, flaps up, gear up,
indicated airspeed 115 knots. “The glide ratio in this configuration is
approximately 2 nautical miles of gliding distance for each 1000 feet
of altitude above the terrain.” Pilot’s Operating Handbook: Beech
Baron 58, p. 3-8]
6.
Figure 2

C. Climb Test Data Reduction
1. Indicated Airspeed (use average of Vi-start and Vi-end for
climb)
2. Calibrated Airspeed (use MATLAB function
AS1Baron58.m)
3. Equivalent airspeed (use MATLAB function AS2.m)
4. True Airspeed (use MATLAB function AS3.m)
5. VT(ft/sec) = VT(knots)*1.688
6. Indicated pressure altitude at start of climb (~4800ft)
7. Calibrated pressure altitude at start of climb (use
MATLAB function ALTBaron58.m)
8. Indicated pressure altitude at end of climb (~5200 ft)
9. Calibrated pressure altitude at end of climb (use MATLAB
function ALTBaron58.m)
10. Change in calibrated pressure altitude for climb: step [9] –
step [7]
11. Convert average outside air temperature for climb from
degC to degR
12. Pmid Atmospheric pressure at the mid point of the climb
(5000 ft) (use MATLAB function atmosphere4.m)
13. Density at midpoint of climb
C. Climb Test Data Reduction
1
Vi (kts)
2
Vc (kts)
3
Ve (kts)
4
VT (kts)
5
VT(ft/sec)
6
Hi-start (ft)(~4800
ft)
7
Hc-start (ft)
8
Hi-end(ft)
9
Hc-end (ft)
10 H(ft)
 mid 
Tmid OAT 5000
11
ft (°R)
R=1716.55 ft^2/(sec^2degR)
14. Density ratio: mid

mid=mid/0
0=.0023769 slug/ft3
12 Pmid (lbf/ft^2)
13 mid(slug/ft^3)
14
Pmid
[12]

RT mid R[11]
mid
(nondimensional)
15. Ts Standard temperature for pressure altitude at midpoint
of climb (5000 ft) (use MATLAB function
atmosphere4.m)
16. Change in altitude for standard day:
15 Ts (degR)
16 Hstandard (ft)
H standard 
17 Wave (lbs)
T mid
[11]
H 
[10]
Ts
[15]
17. Average aircraft weight for test: (Wi+Wf)/2.

D. Climb Test Data Analysis
1.
2.
3.
Put your climb data in a data file called Baron58_CLIMB_data.txt in a
similar format to the example file at the class web site
http://roger.ecn.purdue.edu/%7Eandrisan/Courses/AAE490A_S2006/
Buffer/Climb/.
Run the MATLAB script Baron58_Step_2_Climb_3.m. Use this script
to determine the parameters of the propeller polar, m and b.
The climb velocity that results in the largest angle of climb, γX, occurs
when the climb angle γ given by the following equation is maximum.
4.
5.
6.
7.
  sin 1
H
V t


t
Figure 3
Plot the angle  versus true airspeed as in Figure 2
As demonstrated on Figure 2, find the maximum value of the angle,
 . The true airspeed corresponding to this best climb angle is denoted
as VX. Let WX denote the average weight for the test that produced VX.
Denote mid-x as the density corresponding to the test that produced
V X.
Compare best climb speed with that published in the Pilot’s Operating
Handbook. [Two-Engine Best Angle of Climb VX is 92 knots
indicated airspeed for 5500 pound operation]
Figure 4
E. Max Level Speed Test –Data Reduction
1
ViM (knots)
2
Vc (knots)
3
Ve (knots)
4
VM (knots)
5
VM (ft/sec)
6
HiM (feet)
7
Hc (feet)
8
PM(lbf/ft2)
9
TM (°R)
10
 (slug/ft3)

-
11
12

WM (lb)
E. Max Level Speed Test – Data Reduction
1.
2.
3.
4.
5.
6.
7.
Indicated Airspeed
Calibrated Airspeed (use MATLAB function AS1Baron58.m)
Equivalent airspeed (use MATLAB function AS2.m
VM True Airspeed (knots) (use MATLAB function AS3.m)
VM True Airspeed (ft/sec=1.688*knots)
Indicated prssure altitude
Calibrated pressure altitude (use MATLAB function
ALTBaron58.m)
8. Pressure for the calibrated pressure altitude (use
atmosphere4.m)
9. Outside air temperature (convert degC to degR)
10. Density
M 
PM
[8]

RT M R[9]
R=1716.55 ft2/(sec2degR)
11. Density ratio: mid

=/0
0=.0023769 slug/ft^3
12. Weight of Aircraft. WM = OEW + WfM
F. Determination of Drag Polar Using the Bootstrap Approach
1.
The parasite drag coefficient is found using the best glide data and the
following equation CD0 
W bg sin Gbg
midglideSVbg2
. CD0 only needs to be
computed once from the best glide angle and airspeed, not for every
test point. From your experience does your computed value of CDo
seem correct?
2.

Oswald efficiency factor is found by the following equation
e
4CD0
A tan 2 Gbg
where A is the aspect ratio. From your experience
does your computed value of e seem correct?
3.

Plot the drag polar using the numbers derived in steps 1 and 2 as
shown in Figure 5, where CD  CD0 
4.
1 2
C
Ae L
How do the parameters of the drag polar determined here compare the
values you computed earlier. Which numbers do you think are more
accurate? Why?
Figure 5 Plot of Drag Polar
G. Determination of Propeller Polar Using the Bootstrap
Approach
1. The propeller polar intercept is found by the following equation
2W X2
2
2d 2  midx
d 2 SeAVX4
where d is the propeller diameter in feet, S is wing area in ft 2, e is Oswald’s
efficiency factor, A is aspect ratio and VX is in ft/sec (be sure to make the
conversion from knots to ft/sec). WX is the average weight for the test that
 VX. mid-x is the density for the test that produced VX.
produced velocity
b
SCD0

2. The propeller polar slope is found by the following equation
m
2
 1
2n 0 dW ave
V 2 
 2  M4 
 P0  SeA VM VX 
 C
Where   
, and C is the altitude drop-off factor (=0.12), n0 is the
1 C

rotational rate of the propeller in revolutions per second (RPM/60) at sea level
and where P0 is maximum sea level rated engine power for two engines in ftlbf/sec (2*285 Hp*550). VX is in ft/sec (be sure to make the conversion from
 knots to ft/sec) and VM is the true maximum speed in ft/sec. Wave is the average
of the weights in the tests that produced VX and VM.  is the average of the
densities in the tests that produced VX and VM.
3 How do the parameters of the propeller polar determined here compare the
values you computed earlier. Which numbers do you think are more accurate?
Why?
Figure 6 Plot of Propeller Polar