Mattsz28

iTrader: (1)

Hello All,

I was just hoping to put together a list of useful equations regarding internal combustion motors. I figure it could come in handy when doing any math that may or may not come in handy in this section.

So, I suppose I’ll start

Cylinder Volume = (Pi*(Bore/2) ^ 2) * Stroke
Compression Ratio = ((Pi/4) * (Bore^2) * Stroke + Combustion Volume) / Combustion Volume

Any others would be appreciated. (I've listed 2...)

mr.z28

1+1=3

dont believe me, male+female=male,female,baby

LS1-450

iTrader: (33)

Although, I agree that 1+1=3.........


male + female = broke male w/a chronic headache

3.4camaro

iTrader: (1)

* is a multiplication operator: 2*8=16

^ is an exponential operator: 2^8=256

chevy2808

[I][B]formulas for bore, displacement, stroke
pi=3.1415927
pi/4=.7853982
cylinder volume= pi/4 x bore squared x stroke
stroke= displacement / (pi/4 x bore squared x no. of cylinders)
bore= square root of above formula
displacement(in cc's)= (pi/4 x bore squared x stroke x no.of cylinders)/1000

formulas for compression ratio
cylinder volume= pi/4 x bore squared x stroke
chamber volume= cylinder volume/(compression ratio - 1.0)
compression ratio= (cylinder+chamber volume)/chamber volume
displacement ratio = cylinder volume/chamber volume
amount to mill= (new disp. ratio - old disp. ratio)/(new disp. ratio x old disp. ratio) x stroke

formulas for piston speed
piston speed in fpm= stroke in inches x rpm/6
rpm= piston speed in fpm x 6/stroke in inches

formulas for brake horsepower and torque
horsepower= (rpm x torque)/5252
torque= (5252 x horsepower)/rpm
brake specific fuel consumption(bsfc)=fuel pounds per hour/brake horsepower
bhp loss= elevation in feet/100 x .03 x bhp at sea level

formulas for indicated horsepower and torque:
horsepower= (mep x displacement x rpm)/792000
torque= (mep x displacement)/150.8
mep= (hp x 792000)/displacement x rpm
mechanical efficiency= (brake output/indicated output) x 100
friction output= indicated output -brake output
taxable hp = (bore squared x cylinders)/2.5

air capacity and volumetric efficiency:
theoretical cfm=(rpm x displacement) /3456
volumetric efficiency= (actual cfm/theoretical cfm) x 100
street carb cfm= (rpm x displacement)/3456 x .85
racing carb cfm= (rpm x displacement)/3456 x 1.1

formulas for weight distribution
percent of weight on wheels = (weight on wheels/overall weight) x 100
increased weight on wheels=<(distance of cg from wheels/wheelbase) x weight)> + weight

formulas for center of gravity
cg location behind front wheels = (rear wheel weight/overall weight) x wheelbase
cg location off-center to heavy side= (track/2) - (weight on light side/overall weight) x track
cg height= (level wheelbase x raised wheelbase x added weight on scales)/(distance raised x overall weight)

formulas for G force and weight transfer
drive wheel torque= flywheel x first gear x final drive x 0.85
wheel thrust= drive wheel torque/rolling radius
"g"=wheel thrust/weight
weight transfer= <(weight x cg height)/wheelbase> x g
lateral acceleration= 1.227 radius/time squared
lateral weight transfer= <(weight x cg height)/wheel track> x g
centrifugal force= weight x g

formulas for shift points
rpm after shift= (ratio shift into/ratio sift from) x rpm before shift
driveshaft torque= flywheel torque x transmission ratio

Slvr00Bird

iTrader: (2)

Horse Power (when dealing with FI and psi)

Power = [(NA Power / 14.7) X Boost (psi)] + NA Power

chevy2808

formulas for quarter mile et and mph
ET= (cube the square root of weight/hp) x 5.825
hp= weight/<(ET/5.825)cubed>
weight=(ET/5.825)cubed x hp
mph=(cube the square root of hp/weight) x 234
hp= (mph/234)cubed x weight
weight= (234/mph)cubed x hp
overall gear ratio (manual trans)= (tire diameter/340 mph) x (rpm/mph)
overall gear ratio (automatic)= (tire diameter/335 mph) x (rpm/mph)

formulas for instrument error
actual mph= 3600/seconds per mile
speedo error percent= (difference between actual and indicated speeds/actual speed) x 100
indicated distance= odometer reading at finish - odometer reading at start
odo error percent= (distance between actual and indicated distances/actual distance) X 100

formulas for mph, rpm, gears and tires
mph= (rpm x tire diameter)/(gear rato x 336
rpm= (mph x gear ratio x 336)/tire diameter
gear ratio= (rpm x tire diameter)/(mph x 336)
gear ratio= (rpm x tire diameter)/(mph x 336)
tire diameter= (mph x gear ratio x 336)/rpm

formulas for tire sizes and their effects
tire diameter= 2 x (section width x aspect ratio)/2540 + rim diameter
effective ratio= (old tire diameter/new tire diameter) x original ratio
equivalent ratio= (new tire diameter/old tire diameter) x orginal ratio
actual mph= (new tire diameter/old tire diameter) x indicated mph
indicated mph= (old tiire diameter/new tire diameter) x actual mph

formulas for average mpg and mph
milers per gallon= miles/gallons
miles= miles per gallon x gallons
gallons= miles/miles per gallon
miles per hour= miles/hours
miles= miles per hour x hours
hours= miles/ miles per hour
raceay miles per hour= (miles x 3600)/seconds
seconds= (miles x 3600)/miles per hour

formulas for blood alchahol concentration
BAC= <(ounces x % alchahol x .075)/ weight> - (hours x 0.025)

all these formulas are from the "auto math handbook" hope it helped

Mattsz28

iTrader: (1)

Nice...

The other ones are nice too. Thank you much.

JohnnyC

Engine Power = (hm ) (hc ) (ht) (hv) (ra) (Vd) (N/2) (F/A) (Qhv)


Engine Torque = (hm ) (hc ) (ht) (hv) (ra) (Vd) (N/2) (F/A) (Qhv) (1 / 4pi)

Where hm = Engine mechanical efficiency (power in / power out)

hc = Engine combustion efficiency

ht = Engine thermal efficiency

hv = Engine volumetric efficiency

ra = Air density

Vd = Engine displacement volume

N = Engine speed in radians per second

F/A = Mass of fuel divided by mass of air

Qhv = Heating value of engine fuel

pi = 3.14

RoAdRaGe912

Essentially nothing (except you have to use an approximation for Pi to get to .7854)

(1/2)^2 = 1/4, so once you square the bore and 1/2 everything is multiplication. (Pi*((Bore^2)/4)*Stroke. Pi and 4 are both constants, so divide Pi by 4 = (Pi/4)*(Bore^2)*Stroke = .7854 x bore x bore x stroke

RoAdRaGe912

Are you saying these equations are advanced? The only things more basic than multiplication and division are addition and subtraction...

My attempt at an explanation may have been more confusing. The answer was simply that Pi/4 = .7854, but I tried to show how to transform from one to another.

b0pric01

iTrader: (5)

lol come on, lets show how to find cylinder volume through integration! somebody knows they want to. Don't make me bust out my thermo book for turbine efficiency. I haven't thought about this stuff for a while, I need to go back to school.

ws6chicken

Well our cars do have EFI and a bunch of fancy sensors so:
Some Electrical formulas and units

A 4 year Electrical Engineering degree can basically be boiled down to basically ohms law:
ohm's law
V=IR

V = Voltage
where 1 Volt equals 1000 mV
so in the case of say O2 sensors .451 V is equivalent to 451 mV
I = Current, the unit of measurement is Amperes
where again 1 Amp equals 1000 mA
R = Resistance measured in ohms and the symbol used is omega
1000 ohms = 1 k(ohm)
you don't see m(ohms)

s = Conductance, the unit of measure is Siemens and it is represented as an upside down omega. Usually Siemens are in the micro range. Conductance is literally the inverse of resistance.

Frequency is measured in Hertz (Hz) which is cycles per second, or in data acquisition samples per second. 1000 Hz = 1 kHz; 1000 kHz = 1MHz

C = Capacitance, Capacitors are measured in Farads.

L = inductance, Inductors are measured in Henries

and to b0pric01 we can get really hectic with some good ol' partial differential equations what ever that is.

djyannakis

For the best way to calculate anything car related, check out this neat App for the iPhone/iPod: http://itunes.apple.com/us/app/carcalc/id425600489?mt=8

Wnts2Go10O

iTrader: (12)

what about aerodynamic drag coefficient and such?

SickSpeedMonte

Drag force = drag coefficient × frontal area × air density × velocity^2

I would guess that you would solve for the coefficient, and measure the rest. The coefficient is just a way to compare designs.

Ethan[ws6]

iTrader: (13)

Every formula I've seen for compression raitio on this site calculates for only cylinder volume and chamber volume. Deck height and gasket volume are very important, as well as piston dish/dome.

ACTUAL FORMULA
(CC+PV+DH+GV+SV)/(CC+PV+DH+GV)

CC= Combustion Chamber
PV= Piston Volume (negative for dome)
DH= Deck Height (Bore/2)^2*51.48*Deck Height
GT= Gasket Volume (Gasket Bore/2)^2*51.48*Thickness
SV= Swept Volume (Bore/2)^2*51.48*Stroke

LSOHOLIC

iTrader: (3)

The formulas are easy to come by today with everyone having the internet at their finger tips.

What interests me are the guys who layed down the foundation for which the formulas have legitimacy......

These gentlemen where the first gearheads and they didn't even realize it. They were laying down the laws of thermodynamics and the principles of conservation of energy.
Here is a link to some great info...and of course formulas. http://books.google.com/books?id=1vd...page&q&f=false

Boyles~The ideal gas law. The principle that at a constant temperature the volume of a confined ideal gas varies inversely with its pressure

The mathematical equation for Boyle's law is:
pV=k

p~denotes the pressure of the system.
V~denotes the volumeof the gas.
k~is a constant value representative of the pressure and volume of the system.


Newton~Three laws of motion. 1st law...Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it (Law of Inertia).
2nd law...II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.
3rd law...For every action there is an equal and opposite reaction.

Bernoulli~ Here is another good link with lots of formulas...
http://ecampus.nmit.ac.nz/moodle/mod...t.php?id=48919
The relationship between velocity and pressure. The principle states that an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Bernoulli's principle is derived from the conservation of energy law, which means that the total energy in a system remains constant, just the energy changes states.
When air flows through a divergent duct or a convergent duct at a subsonic velocity it behaves as explained by Bernoulli's theorem. The changes in pressure and velocity do not change the density of the air as long as the air flow remains subsonic.

When the airflow through a duct increases beyond the speed of sound, the pressure-velocity relationship changes dramatically. When supersonic air flows through a converging duct, it cannot speed up, rather it begins to compress. The velocity decreases, and the pressure and density increase. When supersonic air flows through a diverging duct, it expands and the pressure and density decrease while the velocity increases. When supersonic air flows over a surface or through a duct, pressure waves form. There are three different types of pressure waves or shock waves and each affects the airflow differently (Normal, Oblique and Expantion). Almost everything we try to "make better" within our engines is a direct link to Bernoulli and his principles.

And many others............


Thanks............

sxracerb25

iTrader: (6)

How about using cylindrical coordinates and triple integrals? lol ∫∫∫r*dr*dΘ*dz where r is from 0 to radius of the bore, Θ from 0 to 2*pi and z from 0 to the length of the stroke. Then obviously multiply by the number of cylinders. I just had a test over this earlier tonight actually lol

joecar

Yes, you are correct, but you should know from your test that that triple integral simplifies to pi*radius^2*stroke.