Engineering Formula for Automotive Applications

[huafist]

After the discussion Infamous and I had on Fuel Pumps and Injectors, I thought it would be a good idea to post some automotive engineering formulas. I've got tons of these things in my filing cabinet, and I'm going to post them a few a time. Here are some of the most common:

Estimated Power:
BHP = PLAN/33,000
where:
P = BMEP, in PSI
L = piston stroke, measured in feet
A = Area of one piston, in square inches
N = Number of power strokes per minute

BMEP(Brake Mean Effective Pressure)
BMEP = (HP*13000)/(L*RPM)
Where:
HP = Horsepower
L = Displacement in Liters(1 ci. = 16.39 cc = .01639L)

Rod/Stroke Ratio:
A = L/S
Where
L = Rod Length (in inches)
S = Stroke (in inches)

Piston Acceleration:
Gmax = ((N^2*L)/2189)(1+1/(2A))
Where:
Gmax = max. piston acceleration, in feet/sec squared
N = Crankshaft speed, in RPM
L = stroke, in inches
A = Rod Ratio

Piston Travel vs. Crank Rotation:
d = ((S/2)+L)-(S/2 cos X) - L sin [cos-1(S/2L sin X)]
WHere:
S = Stroke (mm)
L = Rod Length (mm)
X = Crank Angle before of after TDC (in degrees)

Piston Speed:
Cm = .166*LN
Where:
Cm = Mean piston speed, in feet per minute
L = Stroke (in inches)
N = Crankshaft speed (RPM)

Piston Stroke Motion:
S = (R cos X)+(L cos Z)
Where:
S = Distance of piston wrist pin from center of crankshaft
R = Radius of wrist pin
L = Length of Rod
X = Angle of wrist pin
Z = Angle of the rod

Compression Ratio:
CR = (V1+V2)/V2
Where:
CR = Compression ratio
V1 = Cylinder volume at exhaust closing
V2 = Combustion Chamber volume

Port Open Time:
T = (60/N)(Z/360)
Where:
T = Time in seconds
N = Crankshaft Speed (RPM)
Z = Port open duration, in degrees

MPH Calculate:
MPH = (RPM*D)/(R*336)
Where:
RPM = Engine RPM
D = Wheel Diameter (in inches)
R = Gear Ratio

RPM Calculate:
RPM = (MPH*R*336)/D
Where:
MPH = Speed
R = Gear Ratio
D = Tire Diameter (in inches)

[Infamous™]

:nice:

[huafist]

Here's a few more - these will allow you to compute the compression ratio of an engine:

CR = (V1 + V2)/V2
Where:
CR = Compression Ratio
V1 = Cylinder Volume (in cubic centimeters (cc))
V2 = Cylinder Head Volume (in cubic centimeters (cc))

V1 = (B^2 * (pi/4) * S)/1000
Where:
B = Bore (in mm)
pi = 3.1416
S = Stroke (in mm)

V2 = HV + DV + V3
Where:
HV = Cylinder Chamber Volume (in cubic centimeters (cc))
DV = Piston Dish Volume (in cubic centimeters (cc))
V3 = Slice (or Squish) Volume (in cubic centimeters (cc))

V3 = B^2 * (pi/4) * (G - DC)
Where:
G = Head Gasket Thickness (crushed) (in mm)
DC = Deck Clearance (in mm)

Formula for Engine Displacement:
D = (B^2 * S * (pi/4))*n
Where
D = Engine Displacement (in cc)
B = Cylinder Bore (in mm)
S = Stroke (in mm)
n = number of cylinders

Formulas for brake horsepower

Horsepower:
HP = rpm x T / 5252
Where:
HP = Horsepower
RPM = Engine speed (RPM)
T = Engine Torque
Torque:
T = 5252 x horsepower / rpm

Brake Specific Fuel Consumption
BSFC = F / BHP
Where:
F = Fuel (lbs/hr)
BHP = Brake Horsepower

BHP loss based on elevation:
L = E/1000 * 0.03 * BHP
Where:
L = BHP loss
E = elevation in feet
BHP = BHP at sea level

[Elroy P. Shagnasty]

first FTF post i've ever bookmarked under "car tech" :-) wonderful post.

[S.P.E.E.D.]

some more fun math for your ass...lol

Air Filter Selection:


An average foam filter will flow 4.38 cfm/sq-in. A good paper filter will flow 4.95 cfm/sq-in. An oiled cotton gauze (K&N) will flow 6.03 cfm/sq-in.

To get your required filtered surface area for a oiled cotton gauze filter use the following formula:
A = CID * RPM

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20839
where A = effective filtering area (square inches)
CID = cubic inch displacement
RPM = rev./min. at max power


Then using the following modifying factors if using an alternative filter media:
A * 1.3767 = required surface area for foam element
A * 1.2181 = required surface area for paper element

Horsepower, ET, and Weight:


A quick calculation for horsepower based on your 1/4 mile trap speed:
HP = (TS/234)3 * race weight or HP = (TS * 0.00426)3 * race weight where HP = Horspower (of course)
TS = 1/4 mile trap speed


This horsepower output is the minumum required for the specified trap speed. It assumes ideal track conditions, weather conditions, traction, and vehicle aerodynamics. It will understate horsepower required at speeds exceeding 100 mph.

Here's some more:
ET = * 5.825
or maybe you want Weight = (ET/5.825)3 * HP


Or try:
HP = weight

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(ET/5.825)3
or for a quick idea of ideal ET assuming good street rubber and decent traction.... ET = 1353

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mph


Volumetric Efficiency:


Engines are occasionally defined as simply an air pump. While this is definitely an oversimplification, your engine's output is based on how much air and fuel it can burn. It's proficiency at burning the air/fuel mixture is defined as it's Volumetric Efficiency. If you know the amount of air your engine can move at a specific rpm you can use this calculation to estimate volumetric efficiency.
Volumetric Efficiency = Actual CFM * 1728

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CID * RPM
or Volumetric Efficiency = Actual CFM

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Theoretical CFM
* 100

Or, if you know your horsepower at a given rpm (the point of peak tq is going to be your max VE) you can approximate your Volumetric Efficiency at sea level by using a variation of the previous Horsepower calculation:
VE = HP * 792001.6

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AP * CR * CID * RPM


Fuel Injectors:


Just as the wrong sized jets in a carb can cause decreeased performance and driveability problems, so can incorrectly sized injectors. The following calculation can be used for approximating fuel flow per injector based on horsepower (HP) and Brake Specific Fuel Consumption (BSFC).

Note:
1) Engine HP must be a realistic estimate.

2) BSFC is determined from engine dyno measurements. It typically ranges from 0.4-0.6 for gasoline engines. A BSFC of 0.5 is a safe initial estimate.

BSFC = Pounds of fuel per hour

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Brake Horse Power



3) The 0.8 multiplier fo the "Number of Injectors" helps derive a practical "Max Injector Flow Rate" for each injector based on an effective real world injector operating pulse time and fuel flow. It is unrealistic to establish the fuel flow to an engine based on an injector operating pulse time of 100% (wide open all the time). This calcuation uses an injector operating cycle of 80%. Some full race engine management systems may operate at 85-95% duty cycle, but extended operation may eventually overheat the injectors and cause irregular flow rates and poor low rpm operation.
Injector Flow Rate (lbs/hr) = HP * BSFC

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number of injectors * 0.8


With a known injector fuel flow rate you can get a rough estimate of the systems capacity by using:
HP = IFR * number of injectors * 0.8

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BSFC

where IFR = Injector Flow Rate (lbs/hr)

Increasing the fuel pressure can often provide increased fuel flow and better atomization. If you know an injector's static (non-pulsed) fuel flow at one system pressure you can find its static flow at another pressure with this:
F2 = * F1 where F2 is the calculated injector static flow (lbs/hr) at the higher pressure
P2 is the fuel system pressure (psi) you want to use
F1 is the injector's static flow (lbs/hr) at it's rated fuel system pressure (psi)
P1 is the fuel system pressure (psi) the injector is rated for

nicw post man I had to track all this stuff down before now its all right here....:nice:

[Autodesk Engineer]

The very first one of those about the filter needs a bit of fixing. You would multiply the CID by 1/2 your max rpms. If you think about it, displacement is measured per cycle, which is 2 revolutions. If you muliplied CID by revolutions, you'd get twice the "flow" or "displacement,"


Furthermore, if you're boosted, you'd multiply by the pressure ratio (and leave VE out of it so that you have a window of error)

Just a thought there...

[S.P.E.E.D.]

of course you have to devide it by half or take the square root of it thus (inches square) I figured if you knew enough to find the formula you would know how to use it

as for forced induction you can do the math but I always allow 10% either way that way you have a 20 % cushion to dial in on

[derangedazn]

Holy Physics Batman....great thread. This will come in handy down the road.