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THESIS

\
ws SF
A THEORETICAL METHOD

OF
DESIGNING THE PORTS OF A TWO-CYCLE
INTERNAL COMBUSTION ENGINE.

THESIS

PRESENTED TO
THE FACULTY OF MECHANICAL ENGINEERING
MICHIGAN AGRICULTURAL COLLEGE

In Partial Fulfillment For The
DEGREE OF

- BACHELOR OF SCIENCE -

BY

Leroy H. Thompson.

East Lansing, Michigan.

June, 1913-6
 

THESIS
[2 ~

“a

\

INTRODUCTION.

The subject of cylinder port design for two-cycle engines
is seeming ly avoided by all writers on internaé combustion
motors. The author of this thesis has searched thru innumerable

standard works for data on tHis subject, without success.

The question arises, "How are the port sizes of our
modern two-cycle engines determined ?" The author has endeavored
in this thesis to present a method of procedure from a theoretical
viewpoint. The problem is one of flow of gases thru an orifice

of variable area, and under variable conditions of temperature,

pressure, specific volume, etc.
A general statement of the functions and operations of

the ports will help in showing the problem in hand.

Near the end of the. expansion stroke of a two-cycle
engine, ( in general practise about 45° to 60° crank revolution
from outer dead center) the piston starts to uncover a belt of
exhaust slots in the cylinder wall. The burned gases in the
cylinder at this point are in the neighborhood of 2000°F.abs., and
under a pressure of 30 to 70 #/sq. in. abs. They rush out thru
these uncovered ports into the exhaust duct, wntil the pressure in
the cylinder has dropped to atmospheric.

When the pressure has dropped to perhaps 18# abs., the
piston uncovers a second belt of ports for inlet of the new charge,
which has been pre-compressed in the crank case, or other wise, to
perhaps 21 # abs. This inlet port in general practise starts
to open at about 25° to 45° before dead center, and is of course
entirely closed at the same angle after dead center. During this

time of perhaps 70° crank revolution, the inlet charge is entering

and forcing out the burned products thru the larger exhaust ports.

The exhaust ports are of course still open for a time after the
inlet port is closed.

2HIS32

 

 

 

—
 

 

Here then is the problem of design: - The inlet port
area varien from zero, to its maximum at dead center, and back to
zero again. During this time, the inlet charge is entering the
cylinder, and the crank case pressure drops accordingly to
atmospheric. | How large must the inlet port be made, and how
soon must it open, for the above events to take place ? Also,
having the inlet port designed, how seon must the exhaust port open,
and how large must it be, so the pressure in the cylinder shall
have dropped below the crank case pressure before the inlet port

is uncovered?

NOTATION: -
For the sake of uniformity, and to avoid confusion, the
following system of notation will be adhered to thruout the work.

T - abs. temp. in Fahr. degrees.

- abs. pressure in pounds per sq. ft.
- abs. pressure in pounds per sq. in.
- crank radius in inches.

- angular motion of crank in degrees.
time in seconds.

- port area in sa. ft.

- port area in sq. in.

- length of port around the cylinder in inches.

re fr YF te QwWid i yw
'

- mean height of port opening in inches, during revolution of
crank between any two given positions.

o - mean height in inches, of port opening from angle at which port.

starts to open, to any other given angular position<«

s - time in seconds for one degree of crank revolution.

W - weight in pounds of total cylinder capacity of gas.

M- weight in pounds of gas escaping from the port per second.

G - weight in pounds of gas escaping in any interval "t".

v - specific volume in cu. ft. per pound of ZAaS
 

THERMODYNAMICS OF THE EXHAUST.
The characteristic factors and constants of the gases

will vary somewhat with the fuel used, method of governing, fuel -
mixture, etc. The gas flow is also affected by a multitude of

other disturbing factors, such as:- Shape of ports, conditions of
the rounded approach, back pressure in the exhaust pipe, volume of
gas behind the port, friction inthe orifice, altitude of the place,

varaitions in load, speed, etc. It is easy to see then, that no

general formula covering all cases can be derived.

The calculations to follow are based on specific values
of the gas constants previously obtained by the author in designing
an alcohol engine. While not applying strictly to any other
fuel, yet the results thus obtained may safely be used as a guide
in designing any ordinary two-cycle motor.

Following are the thermodynamic relations upon which the
conclusions later are based.

Change of specific heat with temperature is given by
Langen's formulae : Cp= Cp + 2T , and Cy=C,, + 2T
The relatipn Pv=BT also holds.

n=—2P = 1 + 2 and B/J = Cp- Cy, = Cp,- Cy

Cy J Cy
The flow of gas thru the ports will follow the adiabatic law. With
specific heat varying as above, this adiabatic relation is given

thus : * log P=K (constant) - 2@ log vy - .4343 ZL
, Cy, | B« Cy.
The following values apply to the exhaust gases of analcohol engine:

P - at point of release - 7200 #/sq.ft. abs.
v - at point of release - 15.9 cu. ft. per pound.

B - 55.95
B/J - .072
Cp, - «2403
Cy - 1683

z—- e0000495
T - at release, from Pv=BT , - 2045 F.: abs.

Substituting these values in the adiabatic formula :

_¢r 22403 0000495." "1229
log 7200=K - vega log 15.9 - «4343 55.95 «.1683

Whence K= 5.5965

7 Wimperis- Internal Combustion Engin®®°

m™
JS
From twelve values obtained from a variety of sources: -
indicator cards, and statements of various authorities, it appears
that a mean value of pressure at release is 50 #/sq,in.abs.,
which is the same as that assumed above.

* Levin says, under proper conditions, the temperature at
release should not exceed 1900°F. (2260° F.abs.)

* From Poole's values, the ordinary value of release temper -
ature is 1500°F. (1960°F.abs.) with the maximum for ordinary engines
not over 2340°F.abs. These instances are given to show the calcul-
ated values preceding to be about those obtained in practise.

Conditions at other points of the release curve may be
obtained by a method of successive approximations, from the
adiabatic equation before given, which for this case becomes :

log P = 525965 - 1-426 log v - .00000228 Pv

Thus : assume v= 33 , find P corresponding. For the
first approximation, disregard the last term of the formula, which
is small. Then, log P= 5.5965 - 1.426 log 33 = 3.431 , P= 2695 .
Substitute this approximate value of P in the last term of the

formula, and solve again’
log P= 5.5965 - 1.426 log 33 - .00000228 « 2695 « 33 = 3.412 ,
whence, P=2580 as a closer approximation. Introducing this value

in the last term, we find the true value of P to be nearer to 2590 .
The temperature is obtained from the relation : Pv= BT ,
2590 x 33 = 55.95 xT ,or T = 1525 F. abs.
Cy is obtained from the formula before given, which for
this case becomes : C,> 1683 + .0000495 x 1525 = .2438
, 2072
n is obtained from the equation : n=l + S436 = 1.2954

Let W= total piston displacement in pounds, then G , the
Weight of gas discharged between v=15.9 and v=33 , is given by

the relation : G= yw (225 18:8) = .518 W

The curves following were plotted from values calculated by the

method just outlined. All the conditions for any given point of the
release period can be found on the curves, if one value is known.

* Levin- Modern Gas Engine & Gas Producer.
t
Kent- Mechanical Engineer's Pocket Book.
 

 

ee

Degrees F. = T i

~
i

Oe E a

 

Lo}
wu

GTA eYs tener Ct Bee) tC Hame) mee LI ce DERE
DURING PERIOD of RELEASE:
| fe |

se BS
8 s BS
: St

v= Shh oe agi et a eed 4 I) >
rs ~
; 3 af ® 8 23 Ss Se

™~

pase orl ete tok

CRITICAL - PRESSURE

Ea

Total Cyl ay st si

= Relative Weight 6 of Gas that bs Tt Seal genet us \

7200

feee é"a2a2a

=P

5
:

et)

bn

re
solute Pressure 3 mes ee. Dae

s

feasts

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Atmakengrs

pizete} e)

i= tae

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The flow of gas thru the ports may be calculated from
the following commonly used formulae, as given in all standard
texts and handbooks.

The so-called "Critical Ratio" of Be is given by the

relation: * B= (2-) a1 This critical ratio shows the
n

pressure relations necessary for maximum discharge for a given
value of the reservoir pressure.
Assuming the back pressure in the exhaust pipe to be
about 15 #/sq.in.abs., or 2160 #/sq.ft.abs., then the value of P,
corresponding to the critical ratio, is found from the foregoing
formula by transposition :
P= 2160 (ast) a-T which for an approximate
mean value of n=1.27 , becomes P,=3920 #/sq.ft.abs.
For all values of P above 3920 , the following
formula applies : # y = aa . Bo 2gn
n+] YT, Blnel)

For all values of P, less than 3920 ., the formula

becomes : ar
M = r\ 26: — * = | (2) -() J

In both formulae the notation is as follows :

 

 

 

M - pounds of gas flowing per second.

F - effective area of orifice or port in sq. ft.

n - mean value of Ch /Cy between PF and BP

P, - pounds per sq-ft.abs. on high pressure side of the port.

P, - pounds per sq.ft.abs. on low pressure side of the port.

T, - Fabs. temperature on high pressure side of port.

v, - specific volume or cu.ft.gas per pound on high pressure side.

B - characteristic constant for the gas, in Pv=BT.

Goodenough- Principles of Thermodynamics. Pg. 253.
# Ditto - Pg. 255 & 256.
7

Let Gsweight of gas discharged in 't” seconds, and let
s=time of one degree of crank revolution in seconds. Then G=Mt ,
and while the crank revolves thru «° , w=

Let R= crank radius in inches.
l= length of port around the cylinder in inches.
h=- mean height of port opening in inches during a crank

revolution of a’.

 

Then Fo 20 » and the formulae for gas flow may be re-stated thus :;
(Above the critical point) hia _ LAA 8 nt) =?

R “IsR -
(Below critical point) ho = (e

 

Sars : Tare -) my

Divide. the pressure range during release into a number

of convenient sections, and find mean values of P,n,v,» G@ ,etc.
for each section by use of the curves pg. 5a.

Apply the above formula to each section in turn. The
results are expressions in terms of 1, 8,R8, andW, all of
which depend upon the sige, speed, and mechanical design of the
engine, and are known approximately or are easily found from data
given for a preliminary design.

Each of the expressions for ree thus found, is a ‘value
necessary to produce the pressure drop indicated during that section
of the curve. } | |

The summation of these quantities gives the "total Rn,
(for distinction called 2°) necessary to get the pressure in the
cylinder down to atmospheric. :

The following table of values were taken from the curves

on P&e Sa, and calculated by the formulae above.
 

 

 

 

 

 

 

 

 

 

 

 

initial mean | mean i final mean G ao = 59 = =<
— —— — ————_}——_ a — 7
15.9 | 16.95] 6620] 6030 | 1.264] «1126 217576 02175 pap
1860 | 1965 | 5370} 4860 | 14267 | .132W| .344 e615"
21.0 | 22.7 | 4360] 4020 | 1.270] .103w| .3215 "| .8830
24.4 | 26.2 | 3550| 3250 | 1.273| .osaw| .2735 "| 1.1565 ©
28.0 | 29.0 | 3100] 2950 | 1.275] .o40w}] .1563 "| 1.3128 ”
30.0 | 31.5 | 2760] 2590 | 1.276] .045W] .190 "| 1.5028 "
33.0 | 34.5 2435 2300 1e277| .0434] .2885 " 1.7913 "
36-0 | 37.0 2200 2117 12279 | .0O24W| .413 " 202043 "
The mean height of port opening "o", during a revolution
of the crank from «, when the port starts to open, to any other

position a,, is a quantity not easily found.
~ Length of connecting rod

on the ratio of =

values of a, and

9 (ax, ~-a, ) -

R

a, @

Length of crank radius

It will depend

» and upon the

The relation is very closely expressed thus:
, R R sint
sin a= sin a, +. Ca, - a, )¢ G7 cos «,- — 4 *eeece

+ wpe. (sin 2a4,- sin 2 q, )

Note:- a, and qa, are expressed in "radian measure". The derivation
will be found in appendix.

This formula is too complex for common usage, and for

convenience the following charts have been plotted from values

computed by the formula.

there-on.

The use of the curves is explained
Also, the value of the actual height of port at any

given crank angle may be found from the curves on Pg- 8c , values

on which were computed from the formula :

rR =

vets a -

R sin w

2L

(also derived in appendix. )

h is the actual height of a port which starts to open a’ from the

outer deéd center.

W, in the above table, we get a numerical value for 2

the required height of port can be quickly found on c

By substituting given values for 1, s, R, and

R
harts pg. 8akb.

X from which

 
fee
WITH PISTON AT OPENING EDGE of PORT.

GORRESPONDING to

: Given the sizes of ports, for example

ort = of crank radius,(17% of se tgek tacts and inlet = 20%
rank radius,(10% of stroke). F other data as follows

In caipun Laceled "C', eee a PCE a cer eee oppes re:
cluan "A"find exh. port’ opens vs . :Lixewis
oluan"A" shows the eens opens nes Caer: 5 s¥s ays ee
alue about 5.7 - This is mean inlet Peet (% of
ultiplied by the angle during which it is open (42°)

an opening, if FCPSe ay: may be easily obtained.
as) eee mean exhaust cio . to the time when inlet star
o

open:= From abscissa mre ttom of chart, up verticall

bE eka meat ere eES with exhaust curve labeled "55°", thence hori-
tally to colunmn"3", which ey: eee mere opening mult
le eich | which it

 
 

ANGLE of CRANK from OUTER DEAD CENTER
ee ee

USEOF THE CHART: o des an inlet port, for ch “mean
epening in : of radius X ation of opening in dezrees" has
been vreviousiy a nett Boe ne Cr ea

eae hee sh blr equsily 1 sides dead center

or 4.5 sti eget up to dead te ie ets)

cojumn e corresponding shows the inlet opens at 37.5°, ire
“= eight of inlet port to be about 17.5% of ecranx errs

Pah suppose the oxthayust re Sian are
at Re He tees CPs he eT Sadao be- bal

nie : ae durati
n col orizo
oe pas ee RT Be re Re eet Meth bP
bo of ¢ Ris ty intersetcion my pretty close to the
ad ed 60°- call it 59. a ere io exhaust
t cr eOtttT: the curve to er extremi
axhauwt Pa SES ER eras bs Pound in

 
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ag

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PCL ec EDT)

3

 

 
INLET PORT CONSIDERATIONS.

The inlet may be a cylinder port, similar to the exhaust
port, uncovered by the piston, or it may be a poppet valve, either
automatic or mechanically operated.

The design of poppet valves and their mechanism is
covered in most standard works on internal combustion engines. In
this investigation, the common two- or three-port engine type, with
pre-compression in the crank case, will be followed out more
especially.

In some types the fuel mixture is pre-compressed, and in
others air alone enters the crank case, the fuel being injected
later. In either case, the laws applying may be assumed without
sensible error to be those applying to air.

Fliegner's equation for air can be used for the inlet
flow where the crank case pressure does not exceed 28 #/sq.in.abs.
Let BR = max. crank case pressure in pounds per sq. ine abs.

This rarely exceeds 21# abs. in practise.
Pp, P., etc. = crank case pressure at any given point of the
inlet period.
PR, = abs. pressure in the cylinder. This is practically
constant at about 15 #/sq.in.abs.
T = abs. temperature in Fahr. degrees in the crank case.

    

Then Fliegner’s equ may be stated :

PLAS - Pil
tT

 

for the mean flow in pounds per

second between P. and P." °
The conditions in the crank case during inlet are approximately

isothermal, with TI. probably 530 F. abs. Then Pv is constant,

RB-FR - wry ~ Gi _
| W

 

or, P y! = percentage of total gas which is
Cc Cc
discharged during the interval from P. to. P. °
R - P Gq” G - q’ ‘ 2"
Likewise, - — = 7’ whence, = == = R p E »which is the
c

percentage of the total gas which escapes during the interval
from P. to PB, .
 

als) = 24) "
-—- = —¥. ip - Bl") at 06 “>

 

 

Then M= FQ SX Pe

h « WCB - Pp.’ )
From which = = &

20 me P

R u 6 Rsl ® a p(=+— - 2)
Substituting P.=2!, Te = 530, Pa = 15, and denoting mean pressure
ai+ by Py » the formula reduces to the form :

ha . 267 WR'- PT) 1

 

R Rs il Py - 15

In this case, "h" is the equivalent mean opening of port,
and a is the total angular duration of that opening (before and
after dead center) or twice the angle from dead center.
Whence, a2 = 2/229 to dead center ) on chart pg. 8a or 8b .

Now divide the inlet curve into sections, each including
a small drop of pressure in the crank case, Pm for each section
being Rte e
Sum up these sectional values of ha getting the total necessary
for the entire curve. One half of this total is the value of oS
to dead center for the inlet.

From this, for given values of W,.R, s, andl, the

Apply the formula to each section in turn.

height of port and angle of inlet can be quickly found from the
charts pg. 8a or &b. |

PS Pe Py a5
21.00 20.00 20.50 114 pee
20.00 19.00 19.50 1260"
19.00 18.00 18.50 1430"
18.00 17.00 17.50 169"
17.00 16.50 16.75 101"
16.50 16.00 16.25 1130"
16.00 15,50 15.75 154"
15.50 15.25 15.375 109”
15.25 15.15 15.20 2060"
15.15 15.05 15.10 084 "
15.05 15.00 15.025 060"

16233 gy oI? RI

ox

“RO

617 wh
 

| I
FINAL CONSIDERATIONS AND DISCUSSION.

In all the foregoing work, no account has been taken of
friction losses, excessive back pressure from the exhaust pipe,
vortex action in the cylinder, poor condition of the rounded
approach to the ports, anh other disturbing factors. All these
will seriously affect the flow of gas, and the designer can only
use his pest judgement regarding them in the problen.

Probably the easiest way to apply such a factor to the
foregoing results, is to add a percentage to the value of W used
in the formulae, which will thus increase the size of port obtained.

The contractien due to popr approach to the ports may
amount to considerable, according to various authorities.

Kent says- 3 to 8% is lost for short well rounded mouthpieces.

20 to 44% +" " with a sharp cornered approach.
Church gives- 44% lost with sharp cornered orifice in thin plate.
25% " " " " short tube.
2% " " well rounded mouthpiece.

Probably for most instances in gas engine practise, from
20% to 40% of the efficiency of the ports is lost thru not having
rounded edges on the approach side. This fact can be entered
in the preceding calcul&étions by giving W in the formulae a value

1/4 to 1/2 larger than the actual piston displacement.

The value given W in the inlet calcul&éions should be
somewhat larger than for the exhaust, in order to compensate for
the extra friction losses in the "passover port" or connecting
passages from the crank case to the inlet port proper. The exact
amount to add for this purpose depends entirely upon the mechanical
design. Goo@ judgement alone can be used in this connection.

For rough average ug$e, the value of ae for both inlet

anti exhaust may be about 2.5% °
8
12

 

 

In the above figure, representing kinematically the
working parts of an engine, ae - ab=d, ae=R vers a~«, ab=L-ka ,
ka=\U' - Ga’, GH = R’sin‘'a« , whence d=R vers a -L + | L* -R*sin* «

d = distance of piston from end of stroke when corresponding

 

crank angle is «°.
The radical term in the above expression is of a form

which cannot easily be integrated.
Expanding the radical by the binomial theorem :

yi 2 ey E R sin’« R? sin* |
2 a _ o£ 2 = — ce. nee aE _— am @0600600 06 e
L - Rosin"a« = Rir-s sing =Ris aL a

The third term in this series will be very small for any

 

 

instance in gas engine practise. Substituting values for re and «
such as to make the terg a maximum within the ordinary limits of

3 4

The error entailed by dropping all terms after the second

inthe above series will then be negligible.
R* sin?
2L

The piston movement "m" from k to any later position xk,

gds engine practise, we get a value for

 

Then daz Rovers « -

is given by the difference in values of d for the two positions.
R*sin*« 1 R‘ sin’ ay
2L 2L

or replacing vers a by (!- cos a ), and simplifying :

 

 

m=d,- d,=R vers a,- R vers a, -

De cos te - cos o, - Rsinta 1. R_sin* o
R 2L 24L
i)

To find the mean equivalent port opening "o", during
revolution from a, when the port starts to open, to any other

position a, ;
Ky

Mean value of ‘o between «a, and OC, = [2-8
be a = a,
Note :- The limits of integration are interchanged to avoid
negative signs, since in this expression qa, is greater than «, .
Substituting value of m :

 

 

A,
£ 2 2 2
mean o = A(R cos «,da - R cos a, dq - Rusin «dq -R sin Onde |
a> a 2 L
x)

In this expression, a, is constant and ay is variable between |
the limits a, and « .

 

Integrating, replacing (cos «a sin a ) by its equal Since eo
(a, - )
and simplifying ° moan = Se Xe 7 = ee e006 e e e

R a
=sin o,- sin «,-(a, - (Fo —- cos q, - Rising, yop(sin 2a, -sin 20, )

«x, and a, in this expression are of course in radian measure.
 

 

 

 
 

 
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2
c=
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—
——
——"
‘_—vT
=a
=—~,
—rT
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