I
THE DESIGN AND CONSTRUCTION OF A
POWERED POGO-STICK
by
EVERETT H. SCHWARTMAN
SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIRMENTS FOR THE
DEGREE OF BACHELOR OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Signature redacted
CertifiedV
W.........Signature
Certified
by
. . . . . . . . . . . .
.
Author
.6. . . . . . .t. . . . . . . .
.
May, 1954
red acted,
01
Thesis Advisor
This thesis consists of the design
and construction of a licuid fuel-air
powered Pogo stick.
The end results are what I believe
to be a properly powered Pogo stick, the
drawings of which are included in this
thesis.
This project is now under construction in the Sloan Laborotory.
The author is especially grateful to
Professor A. R. Rogowski and J. Levingood
for giving so much of their time in regard
to this thesis.
He is also indebted to
them foor their stimulating help in solving the various problems that were
encountered.
Signature redacted
Everett H. Schwartzman
Brookline, Mass.
May 1954
TABLE OF CONTEJTS
Pag e Nuh.'mber
Discriptions of Operating Cycle
.
Introduction
Operating Cycle Analysis
Calculations for Determining Internal Friction
Calculations for Determining Air Drag
/3
Determination of Dimensions
Analysis of Autoignition Through an Energy Approach
Z/
The Complete Analysis of Autoignition of
N-Heptane fuel in the Pog o Stick
Detailed Drawings
S/
Description of Auxilary Devices
4AS
Appendix
1)
Data & Calculations for the Time
Motion Studies
2)
Analysis for Determining the Cylinder
Wall Thickness
rr
3)
List of Standard Parts Used in the Design
50
Xz
INTRODUCTION
The analysis and complete design of a liquid fuel-air
powered pogo stick.
I.
Analysis:
The analysis is divided into the following main
topics:
1)
Description of the operating cycle.
2)
The investigation of the energy dissipated
during the operation due to:
3)
a)
internal friction of mechanism,
b)
air drag.
The determination of size requirements resolved
through the preceding two studies.
4)
The examination of combustion in this mechanism.
This topic is further divided into:
a)
analysis of auto ignition through an
energy approach,
b)
the complete analysis of N-heptane fuel in
the pogo stick, with the necessary timemotion study of mechanism during the
compression stroke.
II.
The Design:
Consists of complete and detailed drawings for the
construction of this device.
Plus:
1)
A description of auxillary and safety devices
used in this mechanism.
2)
List of all standard and supplement parts.
ANALYSIS
Descriptive Cycle Analysis
This device is essentially an Otto engine.
The processes
through which the charge pass are illustrated in Fig. 1 and Fig. 2 and
may be described as follows:
1-2
Compression of charge until explosion occurs.
Takes place
in upper cylinder.
1-5
Charge is drawn into lower cylinder.
Processes 1-2 and 1-5
occur simultaneously.
2-3
Combustion of whole charge takes place very quickly, so it may
assume to explode at constant volume and the mixture of air
and fuel become a mixture of combustion products at a higher
pressure and temperature.
3-4
Expansion of products of combustion--pushing the piston and
connecting rod outward.
5-6
Takes place in upper cylinder.
A small compression of the new charge in the lower cylinder
occur simultaneously with 3-4.
4-1
Exhaust of combustion products out exhaust port into the
atmosphere.
6-1
Takes place in the upper cylinder.
New charge expands into upper cylinder from the lower cylinder
via bypass, pushing exhaust gases out through the exhaust port.
Processes 4-1 and 6-1 occur in part simultaneously; 4-1
usually starts before 6-1.
Fuel-Air Cycle Analysis*
The following was assumed:
1)
*
Actual cycle = .85 of F/A cycle.
For complete description of this analysis, see, The Internal Combustion
Engine, by C. F. Taylor and E. S. Taylor, 1950, Chapter IV.
I
3
- R/FGURE I -eOrro c Yct~
4
UPPER
CYI.ND ER
FWYHU5T
-IATRkg:
BYPRS6
LOWER
-- - ROD
CWIDER
PO(7T
2)
Intake pressure into cylinder = 14.7 psia
3)
Exhaust pressure = 14.7 psia
4)
Temperature of mixture at point 1, Ti, (see Fig. 1) justified later
= 520OR
5)
Fraction of gas left in cylinder from the preceding cycle = .015
6)
Compression ratio of 14 (justified on page 30
)
= f (explained on page'?)
//
Information is obtained from the charts of Thermodynamic Characteristics of
Lean Fuel-Air Mixtures Before Combustion ("Unburned charts"), F/A = .0605 and
Theimodynamic Characteristics of the Products of Combustion of "Lean" Mixture
C8111
and Air ("Burned Charts"), F/A = .0605 (by Hershey, Eberhardt and Hottel).
Process 1-2
Isentropic ComDression of Charge
Tf$2
S/M*7
o r,
.
$
' r,
From above chart, (before combustion)
E,://[(1-fw//s
Then
.g
W/
0
X
__r
and
ior3
From, "Unburned Charts"
r
14
Process 2-3
-
J
A
/
'jxA/
Constant-Volume Burning
.a
P
-W.O
From Combustion Products Chart:
Process 3-4
Isentropic Expansion
[
1/39
2 (0
From Combustion Products Chart:
Process A-1
Products of Combustion Expand to Atmospheric Pressure.
From
Combustion Products Chart:
C = combustion products
f can now be determined
/$k2,
-,
factor is used because of the scavenging
justified on page
(e,)
involved.
It will be
.
The .,
Does not warrent a re-calculationi
Process 6-1, where new charge expands into upper cylinder and mixes with the
residual gas, at constant pressure (P = 14.7 psia).
This calculation is used as a measure for checking assumption 4.
(Temperature of mixture at point 1)
#Slit iNf + -)r
where
= enthalpy of fresh charge
From "unburned chart"
*
.
4does
not warrent re-calculation.
Net work produced during above cycle:
-
W!~a'iIJ
1--~
Calculations of work Required for Scavenging and Pumping:
.
Work required to get scavenging pressure
P2
Assumptions:
P1 = 14.7 psia
2)
P2 = 38
3)
T, = 520*R
psia
required*
-
Process is an isentropic compression.
040e7
From "unburned" charts (F = .0605).
wiAy
0 VV
1/0/5
.
1)
Work Required for Pumping Into Lower Cylinder:
This process is an isentropic expansion.
Starting at the same
conditions as the above process, since the ratio of V
/V2 in the above
process is the exact reciprocal in this process, and since this process is
an isentropic expansion (instead of isentropic compression) the above
results, will be very nearly the same.
The very small difference (if any) will be due to a change in the
properties of the charge during the expansion as compared with the properties
during the compression and they will be assumed to remain constant during
these two different cases.
Thus, the total work required for scavenging and pumping will be
91 Btu/lb charge used for scavenging.
*
Dimension of lower cylinder length is established by this required value
of P 2 (scavenging)
see page
f/.
At this point it becomes necessary to fix some of the design
criteria.
Since the diameter of the bore will be limited by the amount of
acceleration a man can stand, the shape of the upper cylinder will have to
be designed with this in mind.
This in all probability will lead to a
longer stroke than bore in this engine.
This design is a relatively hard
one to scavenge and therefore a scavenging ratio (R) of two will be
chosen.
R=
s
From:
mass of misture pumped/unit time
mass of possible misture retained in'cyl./unit time
Scavenging Efficiency vs Scavenging Ratio of Several Two-Stroke Engines,
prepared by P. M. Ku, 4/6/51, (123.2 - PMK - 4-51)
for a R of 2
where
whe-
Since,
= mass of misture retained in cyl./unit time
mass of possible mixture retained in cyl./unit time
R = 2, the total work required for scavenging and pumping will be
182 Btu,
-' o,
filling the upper cylinder.
Therefore:
."f - /n
3/4
x'(P
0
Actual
From page
it
"V'
we Coomic
.f23 X 77g
Y...
ZPEP
/5.r=/S
has been calculated that .f'EP -.
9',
Wi--o-// r/417 psi
Vs
Actual work available = 144 x 11.14 x 147
= 236,000 ft-lbs
lbs of charge burned
pS.
7--
The Investigation of Energy Dissipated During the Operation Due to Internal
Friction of Mechanism and Air Drag.
1)
Internal Friction of Mechanism
Usually piston speed (S)
2 x stroke x N
is defined by
where
12
S
= piston speed"M
-S
stroke = inches
N = rpm
but this foimula is not particularly applicable to the pogo-stick.
A better approach for the preliminary calculation of piston speed
follows:
Preliminary dimensions:*
1)
Bore = 1 inch in diameter
2)
Stroke = 1.5 inches
3)
Weight of man and pogo-stick = 160 lbs.
Assuming that the height of a hop will be 9 inches or .75 ft. from
the ground.
(On regular pogo-sticks this distance of .75 ft. off of
the ground is a good figure!)
V,
V1 is velocity of pogo-stick when it
Swhere
hits the ground (ft/sec)
2
g = acceleration of gravity 32.2 ft/sec
s = distance of fall .75 ft.
Since, the stroke is 1.5 inches, the acceleration during the stroke
may be computed:
*
.a
,A'4
T
-T=/3,$'
These dimensions will be justified in a later section (page)? ).
They
are proposed here, in order that a rough piston speed can be found, thereby
enabling the prediction of F.M.E.P. (friction mean effective pressure).
J'
/
41
-01
during stroke
3.A
/
From
XI
. 0
From interpolating Fig. 124, page 205, of The Internal Combustion Engine,
by Taylor and Taylor (using curve 1)
FEP= 11 psi
This value is an approximation,
2)
based on a limited amount of data.
Air Drag
The forces due to air drag are calculated as a function of
velocity.
A)
These forces are due to:
Air drag during the vertical -motion. The energy loss/cycle
due to this force remains constant, since it is assumed
that the height of each hop(.75 ft) is constant.
when T = 0 the vertical velocity at the top of the hop = 0
when T = t the vertical velocity at the bottom = 6.96 ft/sec
(calculated on page/t
Since D
(vertical drag force) is proportional to
.
, the average
should be used for drag force calculations.
Reynolds No.:ff
=
density of air
= viscosity of air
= kinematic viscosity for A
= characteristic length, taken to be 1.5 ft
Reynolds No.
9A 9/$
9 t/
(width of person)
-
sJ7 Of
(Y
/Y
Assumptions:
T
-
thickness of man - 9" or .75 ft.
W = width of man - 1.5 ft.
S = 2 x height of hop (2 x .75 ft) - 1.5 ft.
Therefore, area pertinent to vertical motion .75 x 1.5 = 1.13 ft
Coefficient of drag for flat rectangular plate:*
This C
2
W0*E,
is valid for Reynolds numbers greater than 103
-
so it is valid in
the above case.
From shape considerations of the human body it
above C
would be too large.
appears that the
The body is more streamline than a flat
rectangular plate perpendicular to the direction of flow; but considering
all of the odd projections and wind traps of clothes, the above figure is
probably liberal.
Dr
Cp&
1
D
0037
= vertical drag force, lbs.
/s.
Total up-down distance traveled during one cycle = 1.5 ft.
1.5 x -0378 = .0567 ft-lb expended during vertical motion.
*
From, _Egineering Applications of Flud Mechanics, Page 183. By
J. C. Hunsaker and B. G. Rightaire, McGraw-Hill Book Company, Inc.,
19/+7.
B)
Air Drag during the horizontal motion as a function horizontal
velocity.
Vt
=
=
density of air
=
viscosity of air
/
kinematic viscosity for air
X
.
Reynolds No.
at 14.7 psia and T = 80OF
1.9 x 10~
= characteristic length, taken to be 6 ft (average
height of a person)
y./A
b-
Reynolds No. =
h
Assumptions:
Length of man,
Width of man,
, =
I' ,
6 ft.
1.5 ft.
Therefore, man's area = 9 ft 2
Coefficient of drag for flat rectangular plate:*
This C q
J#/IR
S
is valid for Reynolds numbers greater than 103--so it is valid in
above case.
This value for the above (p
is
probably liberal since the
resistance due to clothes has been neglected.
2
~horizontal
drag force, lbs.
L
*
From, Engineering Apolications of Fluid Mechanics, page 183, by J. C.
Hunsaker and B. G. Rightmire, McGraw-Hill Book Company, Inc., 1947.
3)
The determination of size requirements (dimensions)
resolved
through the preceding two studies.
Jf
qgA
Bore is set at 1"
Stroke is set at 1.5"
Height of jump = 9" or .75 ft.
or
at initial
/
Vol. of cylinder
ft. (D4WJ
4
w
-
conditions in- cylinder of
7
'j2
8
P: N 7 Ar/n.
Vol. of charge/lb -
("unburned" charts)
lbs. of charge
2 -7 -:- 060068 /s.
Since
.000S
Actual work available
.lbs.
burned per cycle
= 236,000 ft-lbs
lb, of charge burned
Y34X@ee
4P*
V.OOP
/f.,7
'.
ft-lbs/cycle available to
overcome air friction.
Speed at which pogo-stick will travel at previous given dimensions:
Having a .75 ft. jump (vertical) the cycle time can be calculated.
2EI*
[72S
~
'
: C-r7-01
=~ Z/6
ntc.
(1
Allowing for both "up and down" time
T cycle = .432
The time that the stick remains on the ground during combustion is small,
and therefore neglected.
YApo
Distance between hops
energy dissipation due to vertical motion
.0567 ft-lb/cycle
x Y.7 + .0567 = ft-lbs/cycle (diosipated by air drag)
.0126
Vol.*- OS
.~~01
-/ /0.
w-&y$.$1
/4e ?
/
.'
.004
or
..
=f.6G0
8.5 M.P.H. is speed at which pogo-stick will travel with .75 ft. high hops.
The following is a calculation of how high the stick will go
before the "up and down" energy dissipation due to air friction is equal
to the energy output of the engine.
The horizontal velocity is equal to
zero.
From previous calculations
Dv'.T oo
V
7 V,
, but the average velocity is used in the above case, and is:
V
Dv
O
fY
Energy =
Energy =
r)
wherefr
.7X3).
59
/ V/
16S
(total distance) x 2.V
64.4 k.oo S7
2
=a'
, Off 7
,o=/.F
t .& ..
(up and down motion)
Determination of Scavenging pump piston diameter (see sheet
Rs
Requirements:
ffl
9N
2.
Vol. of upper cylinder = 1.18 cubic inches
2 x 1.18 =
2.36 cubic inches.
=
amount of pumping volume needed.
Since diameter of connecting rod is 1" (same as piston diameter-see sheet 1)
and the length of the stroke is 1.5", let D 2 = pumping piston diameter.
Pumping Vol. =
.J4
a
Nw' A
ix ~na l/
Afi
9
inches
The actual design uses a '2 = 1.75"
Determination of Vol. difference needed during pumping stroke of the
scavenging piston in order to obtain a scavenging pressure of 38 psia.
(This
gives the dimension of x (Fig. 3) which is needed as design criterion).
Effective scavenging area
fig
.
(annular disk - see Fig. 3)
= 1.61 sq. inches.
Vol. of Bypass (see sheet f
)
Ws; /(()
=1 x 4.75 x 10 x 2
= 1.2 in3 (Vol. of both bypasses)
H
'1~~
, 4",
Lowt CAYLIpt,
Rt9(MUIO
A
moo
DISK)
X16,04C.-3
P
V
= 14.7 psia
= 12
From unburned charts.
For
P2
V2 = 6.5
38 psia
Therefore:
/,4
+.
Or
9 (/ . y
Y . .. ./.2
/'/ Op
RF 3)
_
/At
.2 -/
e 2R.
AZabL
2.2
s"~q
Z
* .--
,
V 1W A~
N ME
The actual design uses x = 1.00 inch.
of specifications used to give 10.7 ft-lbs of work per cycle, with
R
2, and a scavenging pressure of 38 psia.
Piston bore = 1 inch
Length of stroke = 1.5 inches
Scavenging piston bore = 1.75 inches
Distance between top of bypass port to bottom of lower cylinder = 1 inch.
(see detail drawings)
4)
The Examination of Combustion in this Mechanism.
The complete charge is auto-ignited through the high
compression obtained in this mechanism.*
Therefore, no accessories are needed
for ignition.
* For a complete analysis of auto ignition see:
M.I.T. - Ethyl Corporation,
Annual Report No. 6, July 1952-July 1953; and M.I.T. - Ethyl Corporation Combustion Project Progress Report No. 17, covering the period June 15, 1953 to
August 15, 1953.
As a first
assumption, it
was decided that a compression ratio of
11 was needed for auto-ignition of Benzene.
Since all the information
pertaining to the self-ignition of N-heptane fuel was available - this fuel was
used instead.
It
was later found that for auto-ignition of N-heptane
in the pogo-stick a compression ratio of 14 was necessary.
(analyzed on
page$O')
The preliminary approach to the auto-ignition problem was carried
out with the assumption that the compression ratio of 11 was necessary, but
this ahalysis did not include the effects of time.
A later and more detailed
study of the fuel properties of N-heptane showed that a compression ratio of
14 was required (included time effects).
This section will be divided into two sections:
a)
Analysis of auto-ignition through an energy approach.
(A compression ratio of 14 will be used, since it was
later found to be necessary; even though the original
energy approach used an r = 11.)
b)
A complete analysis of auto-ignition of N-heptane--which
determined the required compression ratio (14).
This
analysis included time effects on the fuel and therefore
required a time-motion study of the pogo-stick during
operation.
An Energy Approach Using a Compression Ratio of 14
At the initial
state of the charge:
Pre /Y. 1 Pim
T,
= XAO*OR
Vp
At a compression of 14, assuming an isentropic compression ("unburned charts",
F/A = .0605)
P VS7?0
Hag
=A4 .
X,,- ,'AG
N
ir.e .
2*
'6H =2( Z-'37 =;.S
Btu/l.0605 lbs of charge
o9r r
.MrT
2/f
Btu/lb of charge
Under the best possible scavenging conditions
.0000568 lbs. are compressed
therefore 214 x 778 x .0000568 = 9.45 ft-lbs needed are needed for compression.
Under the above conditions (Q3vi)
the amount of residual gases compressed
is zero (f= 0).
The amount of energy required for pumping during the compression
stroke is calculated and added to the above figure (7.5 ft-lbs), since the
above sum of energies will be needed to reach the state required for autoignition.
Pumping energy used during compression:
$Bu.n. of ComAG&
calculated on page /0since
R -,
2 x .0000568
.0001136 lbs. of charge pumped.
778 x 40.5 x .0001136 = 3.6 ft-lbs needed for pumping of charge during
compression.
Total energy = 9.45 + 3.6 = 13.05 ft-lbs.
If the man and pogo-stick weight 160 lbs.
AOx
3. Ox -ft.-/,
/.?. ara/4 f
0,
where x is height of jump needed
to ignite the charge..
O)f12:.99
/N
cHs.
From this examination it
appears that self-ignition will occur
without excessive jumping - and that this type of ignition is "perfectly"
9,iited for its present application.
) A Complete Analysis of Auto-Ignition of N-Heptane Fuel in the Pogo-Stick.
For this analysis a time motion study of the compression stroke
is needed, and follows:
Displacement of
piston,.I
Aa
-
A
-
,
r
P E N To
i
ATM$P#Rng
PT|. A7pSAs
LOWER
CYU/NDL.
RN (IL4j E~r~rCLA
P(
Figure 4
'0
S Mass of pogo-stick and man,
v
a
t
The calculation of the deceleration of pogo-stick due to the compression
and pumping forces vs. piston displacement:
poth
)direction
0)
(x)
Fjw(/'4C
-4)Rg
forces act in the same
and decelerate the pogo-
stick (see Fig. 4).
The displacement is divided into 15-.1" increments and the
average force (F1 + F2 ) occurring during each increment is used to calculate
the average acceleration occurring during the displacement of one
increment:
(3)
4
L-
P
is gravitational accelera-
where
tion of the earth.
Time = 0, when ICr0
R
A, 7/ ,,
v (0
then the piston is displaced upward .1" (see Fig. 4) --'14
From the formula
PV
where n = 1.32 for N-heptane,
I
.
/7
(i)
the corresponding pressure P
can be calculated,
by using the change in V due to the displacement of the piston.
Thus,the forces are found and it
is possible to plot the
acceleration vs piston displacement by using equations (1), (2), and (3).
This has been done and the corresponding calculations and data
are in the appendix, pagef..
See Fig. 5 for the plot of acceleration vs piston displacement.
From Fig. 5 the average acceleration for each increment is found, and from:
v
+rs
where a
= ave. accel. of each increment
V2
= vel. at the end of each
V
= vel. of preceding increment
"
0
S = width of increment (.1")
initial velocity = 0
CC[L fAER67c/Y/
H-
K. P/S 40T1A D/SPLCMENT dm 4 r,,y
COMP f SS/ON
-
.-.
77~~7L
-
- --
-
.
-
~~IILL1
K}i.I77L 1 ii77J7
N*1
* 1+1
4-
IjA
1-
.
N lip
44
-t
~
I
_
_
--I
-l
-I
A~/i~t
--1-Li
/9
46I
LY
7t2
10
DdAl
The velocity vs. piston displacement curve is obtained.
See Fig. 6.
The
calculations are in the appendix on page.fY.
From Fig. 6 the average velocity over each increment is found, and
from:
Vt
s
where t = time - secs.
V =average velocity over each
increment.
S = width of each increment.
The time required for the piston to travel over each increment is
found.
Thus, the time required for the piston to travel to any displacement
7',
is the sum of the "times" of each increment through which the piston has
travelled while getting to position 2
(at the top of the graph)
.
These times are recorded on Fig. 6
and correspond to the time required by the piston
to reach the place where the time is recorded.
(Time is in milli-seconds.)
A plot of pressure vs idsplacement is also recorded on the same
graph, with their corresponding temperatures.
An auto-ignition-delay map for N-heptane and air, F/A
supplied in this report, Fig. 8.
= .066 is
This "map" shows the time required for
auto-ignition of the fuel-air mixture at different states of pressure and
temperature.
This above mentioned time is referred to as delay time.
On an overlay of this map, Fig. 7, a plot is drawn of the temperature
vs. pressure of the mixture which occurs in the pogo-stick.
On this some plot
the cycle times corresponding to the particular states are also shown.
(Reference to Fig. 7 and Fig. 8, will elucidate the above description.)
A
corresponding delay time )from Fig. 8 can be correlated with each cycle timet,
recorded on Fig. 7.
See chart on Fig. 9.
C~)
C')
(J
K
(%J
N
K
ci
K
N
44
-
+.
--
-r
7--
-7-I
-t7--7
T-f
:4::
4;
+
~4I-iF4-~4 44
,
4T
444444-t 4-4.44-
t4
-+--7~O~
i-4~i+f4-H-4,
~t44
7->
-7
4
+4+4
1
7tji>
VP>
Vt
4J7
t
ft 7 1:>-'
4171i~4
~VJ77
.44
4
-z
I
Ldn
4-L4 4!tl + 1
-t -t ;I.i'~1~
-
-
-#
I
PRE
FUEL
SURE -TEMPCR AruRC -TIMC
a
N- HE(PTAN( *N
I
/'00-
1500
to0
gooo
/0001460LL
TIME
'S
/WA
a3-52&#c.v
ED
90
7
o
t1100
M/A/-SfeNDS
co
-CYac
rmix~Ih
TME
-~
2.00
300
400
4r ^^OAAA
0 uQw
x
i
I
+
/0.6
1800
(1) 1200 RPM
S.A.= 7.5*
C. R. = 6. 18
Pi = 23"
/0.4
Hg
ENG/NE T/ME
PRESSURE -TEMPERATURE-TIME
M/LLISECONDS
PATH
END
GAS
FUEL = N -HEPTANE
Abs
Pe = 30"
Hg Abs
Ti = 160* F= Tj
KNOCKING
1700
OF
X =MEASURED KNOCK
+=PREDICTED KNOCK
ARRIVAL
4M=FLAME
C.R.= 3 56
Pi = 36.7'
Hg Abs
Pe=12 "
Hg Abs
Ti = 160*F Tj =168*F
NON-KNOCKING
1600-
1500,
----
(2)400
RPM
S.A.=11.30
C.R. = 3.56
Pi =29.6" Hg Abs
" Hg Abs
0. IPe = 8.0
Ti = 160*F Tj=1200 F
CK IN G
.KNO
0
0
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2 2.
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.
82
ENG/NE
T/ME
MILLISECONDS
1100
20.2
__._
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400
-.
4
C.R. = 3. 56
Pi = 36.7" Hg Abs
/4.8
I
10001
1/
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S.A.= 100
- 4-Pe=I
I
160 0
F
Ti=
KNOCKING
80 v 0' /8 ./-
/6.7
Hg Abs
Tj=136 0 F
N - HEPTANE
F/A = 0.066
A3/N.L
AUTOIGNITION
AIR
DELAY
900
0
100
200
300
p ( psi a)
Figure 1.
400
500
600
HF-F+4--4--I
414 FR
H+4+f4 4
T-Fl
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30
With this information the cycle time at which auto-ignition occurs
in the pogo-stick can be found.
Procedure:
a)
First
b)
Then, a unit area is defined as follows (
is plotted vs. t(Fig. 9).
/
,
this is seen
by the shaded "'squaret" area in Fig. 9.
c)
A vertical line is drawn from the plot of
vs t to the
abscissa, so that the area encompassed by the plot, abscissa, and
vertical line will equal the defined unit area.
The above is
recorded in Fig. 9.
The intersection of the vertical line with the abscissa gives the
corresponding cycle time at which auto-ignition will occur*-89.45 milliseconds.
From Fig. 6 it is seen that when the cycle time is 89.45, the
piston displacement is 14
of the total stroke, or
15.
14.2 x 1.5 = 1.42 inches
15
as compared with .99 inches obtained from the energy analysis.
compression ratio required for auto-ignition is 14.2
Thus, the
All frictional effects
are assumed to be small, and are, therefore, neglected in the time-motion
study needed in the previous analysis.
----------------------------------------------------
* The complete theoretical analysis of this procedure is given in: M.I.T.
Ethyl Corporation, Annual ReDort No. 6, July 1952-July 1953; and
M.I.T. - Ethyl Corporation Combustion Project Progress Report No. 17,
covering the period June 15, 1953 to August 15, 1953.
-
-
II.
Design
This section includes:
1)
The complete and detailed drawings for the construction
of this device.
2)
The description of auxillary and safety devices used in
this mechanism.
3)
List of standard or supplement parts used in the pogostick.
311I
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2)
The description of auxillary and safety devices used in this mechanism.
A)
The upper piston (Part 9):
In reference to sheet 1A the position of the upper piston is
seen.
A heavy spring (Part 18) keeps a back pressure on this
piston (Part 9) during the operation of this mechanism.
By changing the compression in this spring (accomplished by
placing spacers between Part 10 and the spring (Part 18), the amount
of energy utilization during the operation of this mechanism can be
controlled.
During combustion in the upper cylinder high gas pressures are
reached (order of 2000 psia).
This pressure exerts a force on the
upper piston, which in turn displaces it upward and compresses the
spring (Part 18).
If the upper piston is displaced high enjoughexhaust portswill
be uncovered (see Part 2 for details), thus allowing some of the
high pressure gases to expand into the atmosphere and thereby
accomplishing less useful work in respect to driving the mechanism
as compared with the case when the upper exhaust ports are not
uncovered during the operation of the mechanism.
In this manner the device can be adjusted to suit people of
different weights.
B)
Bleed values (Part 13):
In reference to sheet 1A the position of these values (Parts 13)
is seen.
During operation of the pogo-stick a high downward velocity of the
piston occurs while combustion is taking place in the upper piston.
Upon completion of the power stroke, the piston motion has to be
stopped.
This is accomplished by compressing gas in the lower part
of the power cylinder.
In order to keep the piston in the downward
or cocked position after the power stroke, it
becomes necessary to
bleed some of this gas into the atmosphere-to prevent the upward
"bouncing" of the piston caused by the compressed air in the lower
part of the lower cylinder.
This is accomplished and controlled
by the needle values (Part 13).
C)
Spring (Part 17):
In reference to sheet 1A, the position of this spring (Part 17)
is seen.
This spring keeps the piston in the cocked position so that the
compression and power stroke will occur at the desired time--when
the operator and pogo-stick hit the ground.
Because of the position of the spring in the mechanism it
enables the implement to be operated as a normal pogo-stick when
the fuel supply is cut-off.
50
List of standard or supplement parts used in the pogo-stick.
Part No.
13
No. Required
Description and Part No.
2
Stromberg Adj. Jet
2
For carburetor
Zenith Adj. Jet
2
P12802
-
3)
C71-21
Compression male connector
Weatherhead
68-2
For injector - compression union
Weatherhead
7
1
62-2
Taper pin #5
1 3/4" long
Taper pin #6
2 3/4" long
1
Spring-size will be detemined by
17
1
Erperiment upon Completion of' Pogo-stick
Spring-size will be determined by
Experiment upon Completion of Pogo-stick
III.
Apoendix
1)
Data and calculations used for the Motion-time graphs.
2)
An analysis of the stresses encountered in the cylinder
during combustion--which leads to its
design dimensions.
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2)
Calculations for determining the cylinder wall thickness.
Material:
1020 cold rolled steel.
Ultimate tensile strength -55,000 psi (eu.7t')
Endurance limit in reverse bending 27,000 psi(E..)
U.7
(.rroo
Psi)
0 0a PS.)
E.L (
ps.)
.1 (20
yr S (r-Ooo
PS)
.
Goodman Diagram
Useful endurance limit = 34,000
Since cylinder wall stresses will be only in tension, from Goodman's
diagram an effective endurance limit of 3YOOfpsia will be used.
axial stress = 0
hoop stress =
PO:
P = cylinder pressure
Z.C
'3I/0V
(psi)
=
r = cylinder radius
(inch)
-t
t = cylinder wall thickness
(inch)
t'/I::
31/600 X
F = safety factor (4)
S
= endurance limit
(psi)
A cylinder wall thickness of .125" is actually used.
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