The design and construction of a powered pogo-stick

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

May, 1954

Author

Signature redacted

CertifiedV

W...Signature

red acted,

Certified by . . . .

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

construc-tion 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

solv-ing the various problems that were

encountered.

Signature redacted

Everett H. Schwartzman

Brookline, Mass.

TABLE

OF CONTEJTS

Pag e Nuh.'mber

Introduction

Discriptions of Operating

Cycle

.

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}

_Xz

Motion Studies

2)

Analysis for Determining the Cylinder

rr

Wall Thickness

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:

a) internal friction of mechanism,

b) air drag.

3) 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 time-motion 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.

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. Takes place in upper cylinder.

5-6 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. Takes place in the upper cylinder.

6-1 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/FGUR

E

I

-eOrro c Yct~

4

UPPER CYI.ND ER FWYHU5T PO(7T -IATRkg: BYPRS6

LOWER CWIDER

-- - ROD

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

=

f (explained on page'?)

6) Compression ratio of 14 (justified on page

30 )

//

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

S/M*7

Tf$2

r,

.

' $

o r, From above chart, (before combustion)

E,://[(1-fw//s .g W/ 0

Then __r X

From, "Unburned Charts"

14 - J ' jxA/

Process 2-3 Constant-Volume Burning

.a P

-W.O

From Combustion Products Chart:

Process 3-4 Isentropic Expansion

and ior3

r

A

/

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,

-, Does not warrent a re-calculationi

The ., factor is used because of the scavenging

(e,)

involved. It will be justified on page

.

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 f iN + -)r

where = enthalpy of fresh charge

From "unburned chart"

.*

4does

not warrent re-calculation.

Net work produced during above cycle:

1--~

Calculations of work Required for Scavenging and Pumping:

Work required to get scavenging pressure P₂.

Assumptions:

1) P₁ = 14.7 psia

2) P₂ = 38 psia - required*

3) T, = 520*R

Process is an isentropic compression. From "unburned" charts (F = .0605).

040e 7 wi Ay 0 VV 1/0 ./5 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 P2 (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= mass of misture pumped/unit time

s mass of possible misture retained in'cyl./unit time

From: 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 = mass of misture retained in cyl./unit time

whe - mass of possible mixture retained in cyl./unit time

Since, R = 2, the total work required for scavenging and pumping will be

182 Btu, -'

o

, filling the upper cylinder. Therefore:

."f - /n

3/4

"V'

we Coomic

x'(P 0 Y... .f2 3 X 77g

Actual

ZPEP

/5.r=/S

pS.

From page it has been calculated that .f'EP -. 9',

Vs

W

i--o-// r/417 psi

Actual work available = 144 x 11.14 x 147

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) is defined by

2 x stroke x N -S = piston speed"M

S 12 where 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,

Swhere V₁ is velocity of pogo-stick when it

hits the ground (ft/sec)

g = acceleration of gravity 32.2 ft/sec2

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).

From J' 41

/

sJ7 Of

during stroke

-01

_3.A

_/

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, based on a limited amount of data.

2) Air Drag

The forces due to air drag are calculated as a function of

velocity. These forces are due to:

A) 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

(Y

= characteristic length, taken to be 1.5 ft (width of person) Reynolds No. A

9 9/$

-/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 2

Coefficient of drag for flat rectangular plate:* W0*E,

This C is valid for Reynolds numbers greater than 103 - so it is valid in

the above case.

From shape considerations of the human body it appears that the

above C would be too large. 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 = vertical drag force, lbs.

0037 /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.

Reynolds No.

=

Vt = density of air

= viscosity of air

/

kinematic viscosity for air X . 1.9 x 10~ at 14.7 psia and T = 80OF

= characteristic length, taken to be 6 ft (average

height of a person) Reynolds No. =

b-

h y./A Assumptions: Length of man, , = 6 ft. Width of man, I' , 1.5 ft.

Therefore, man's area = 9 ft2

Coefficient of drag for flat rectangular plate:* J#/IR S

This C q 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.

3) The determination of size requirements (dimensions) resolved through the preceding two studies.

Jf Bore is set at 1" qgA Stroke is set at 1.5"

Height of jump

=

9" or .75 ft.

Vol. of cylinder

/

or

- w

4

ft. (D4WJ

at initial 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 .lbs. burned per cycle

Actual work available

=

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.

~

[72S

2EI*

' : C -r7-01

(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.

Distance between hops

YApo

energy dissipation due to vertical motion

.0567 ft-lb/cycle

.' .0126 x Y.7 + .0567 = ft-lbs/cycle (diosipated by air drag)

.~~01

Vol. *- OS

w-&y$.$1

/4e

?

-/ /0.

/

.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

7 V,

V V , but the average velocity is used in the above case, and is:

fY

Dv =a'

O

,

Off

7

16S

Energy = r) wherefr (total distance) x 2.V (up and down motion)

Energy =

.7X3).

₅₉

64.4

k.oo

S7

2

/ V

/

,o =

/.F

tt.&

..

Determination of Scavenging pump piston diameter (see sheet ffl

9N

Requirements:

Rs

_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 D2 = pumping piston diameter.

Pumping Vol.

=

.J4

a

Nw' A

ix

~na

l/

A

fi

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

. Ws; /(()

(annular disk - see Fig. 3)

= 1.61 sq. inches.

Vol. of Bypass (see sheet f )

=1 x 4.75 x 10 x 2

= 1.2 in3 (Vol. of both bypasses)

Lowt CAYLIpt,

Rt9(MUIO

A

DISK)

H

'1~~

moo

, 4",

X16,04C.-3

P = 14.7 psia

For P2 38 psia

V

=

12

V2

= 6.5

From unburned charts.

Therefore: _/,4 +.

Y . .. ./.2

9 (/ . y

_

/-

.2 -/

e 2R.

2.2

* .--

,

AZabL

s"~q

Z

N ME

V 1W A~

At

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

Combus-tion 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

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

2/f

Btu/lb of charge

.MrT

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

(Q

₃

vi)

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

auto-ignition. Pumping energy used during compression:

$Bu.n.

of ComAG&

calculated on page

/0-since 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.-/,

where x is height of jump needed

/.?. ar a/4

f

to ignite the charge..

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

i

A

-r

-

,

P E N To

ATM$P#Rng

PT|.

A7pSAs

LOWER CYU /NDL.

RN

(IL

4j

E~r~rCLA

P(

Figure

4

Mass of pogo-stick and man,

v

t

a

'

0

S

The calculation of the deceleration of pogo-stick due to the compression

and pumping forces vs. piston displacement:

poth forces act in the same

0)

)direction

and decelerate the

pogo-(x)

Fjw(/'4C -4)Rg 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

P

L-

where is gravitational

accelera-tion of the earth.

R A, 7/ ,,

v ( 0

/7 Time = 0, when ICr0

then the piston is displaced upward .1" (see Fig. 4) --

'14

.

From the formula

P

V

I

_(i)

where n = _{1.32 for N-heptane, 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:

0

v

+rs where a

=

ave. accel. of each increment

V2

=

vel. at the end of each "

V = vel. of preceding increment

S = width of increment (.1")

CC[L fAER67c/Y/

K. P/S

40T1A

D/SPLCMENT

dm

4

_r,,y

COMP f

_SS/ON

~~IILL1

-H-

-.-.

-

-

- - -

- .

-t

~

--I

-l

A-

-I

N*1

~/i~t

/9

77~~7L

K}i.I77L

1

ii77J7

4---1-Li

LY

* 1+1

I

44

_

I

_ IjA

1-7t2

. N lip 10

DdAl

46

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 . These times are recorded on Fig. 6 (at the top of the graph) 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

=

.066 is supplied in this report, Fig. 8. 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.

~4I-iF4-~4 44 i-4~i+f4-H-4, 4 +4+4

4-L4

4

_!tl

+

1

~t

44

-t

-t

;I.i'~

1

~

-tji>

7

₁

4171i~4

4J7

+ 4;

VP>

4

C~)

C')

(J

K

(%J

N

K

ci

K

N

44

-Vt

Ldn

+. -r

~VJ77

:4:: -t -z -7-I .44 7->

-t7--7

-#

--

t4

4T

-+--

-7

-7~O~

7--444444-t

4-4.44-f

_t

7

1:>-'

I T-f ,

PRE SURE -TEMPCR

AruRC

-TIMC

FUEL

a

N-

HE(PTAN(

_*N

_I

/'00-1500

to0

gooo

/0001460LL

_{TIME 'S}

_/WA

_M/A/-SfeNDS

a3-52&#c.v

co

rmix~Ih

E D

-CYac

TME

90

7

-~

4r ^^OAAA

I 0 uQw

2.00

300

400

o t1100

1800

1700

1600-1500,

1400

100

200

300

p ( psi

a)

400

500

600

Figure 1.

x

i

I

+

/0.6

(1) 1200 RPM

S.A.= 7.5*

ENG/NE T/ME

PRESSURE -TEMPERATURE-TIME

C. R. = 6. 18 /0.4 M/LLISECONDS PATH OF END GAS

Pi = 23" Hg Abs FUEL = N -HEPTANE

Pe = 30"

Hg Abs

X =MEASURED

KNOCK

Ti = 160* F= Tj

+=PREDICTED KNOCK

KNOCKING

4M=FLAME

ARRIVAL

C.R.= 3 56

Pi = 36.7'

Hg Abs

Pe=12

"

Hg Abs

Ti = 160*F

Tj =168*F

(2)400 RPM

S.A.=11.30

NON-KNOCKING

_C.R.

₌

_3.56

Pi =29.6"

Hg Abs

----

0

.

IPe

= 8.0

" Hg

Abs

Ti = 160*F Tj=120

0

F

0

0

.KNO

C K I N G

zm

u SX29.6 _22.9 _ 12 5 _{+ 2 .} >292. 2 2. _j 05-J

00..5

9

-7 -17.11.0 z _{1 /.6,>} 16. 2 50 0.0 5.6,

020.9

10( . 82 ENG/NE T/ME

MILLISECONDS

__._ 20.2

(3)600 RPM

S.A.= 10

0

400

-.

4

/4.8

C.R. = 3. 56

I

..

1/

Pi

=

36.7" Hg Abs

- 4-Pe=I I Hg Abs

Ti= 160

0

F

Tj=136

0

F

N - HEPTANE

AIR

8 0 v ' /8 ./-0 /6.7

KNOCKING

F/A = 0.066

A3/N.L

AUTOIGNITION DELAY 0

F-1300

1200

1100

10001

900

0

HF-F+4--4--I 414FR H+4+f4 4

~t~i'U~2J

-, If

T-Fl

I

I--

---ILI_-Iv1177

4 i 4! ad _

__

4'7

1

*I .4 :

~

- __ 7 71-K-~~i93

j

-3j 13.7.~.

I

Ti

i~44

--11 7 7 - 1 -. .

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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 is plotted vs. t(Fig. 9).

b) Then, a unit area is defined as follows (

/

, 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 milli-seconds.

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. Thus, the

compression ratio required for auto-ignition is 14.2 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

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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

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

50

3) List of standard or supplement parts used in the pogo-stick.

Part No. 13 No. Required 2 2 2 1 1 1

Description and Part No.

Stromberg Adj. Jet P12802

For carburetor

-Zenith Adj. Jet C71-21

Compression male connector

Weatherhead 68-2

For injector - compression union

Weatherhead 62-2

Taper pin #5 1 3/4" long

Taper pin #6 2 3/4" long

Spring-size will be detemined by

Erperiment upon Completion of' Pogo-stick Spring-size will be determined by

Experiment upon Completion of Pogo-stick

7

III. Apoendix

1) Data and calculations used for the Motion-time graphs. 2) An analysis of the stresses encountered in the cylinder

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Material: 1020 cold rolled steel.

Ultimate tensile strength -55,000 psi (eu.7t')

Endurance limit in reverse bending 27,000 psi(E..)

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