Paging Larry Meaux and others - Engine math

[J-Rod]

Just wondering if folks had formulas they'd like to share on calculating the hows and why's of engines...

Larry has been great on posting formulas for making calculations. Jsut wondering if we should make a thead to collect them in all in, and if folks had any they wanted to share.

For instance...

ICA = advertised Intake Closing timing (Angle) in degrees ABDC
RD = Rod horizontal Displacement in inches
RR = Rod Distance in inches below crank CL
PR1 = Piston Rise from RR in inches on crank CL.
PR2 = Piston Rise from crank CL
1/2ST = one half the STroke
DST = Dynamic STroke length to use for DCR calcs

RD = 1/2ST * (sine ICA)
RR = 1/2ST * (cosine ICA)
PR1 = sq root of ((RL*RL) - (RD*RD))
PR2 = PR1 - RR
DST = ST - ((PR2 + 1/2ST) - RL)

Cylinder volume = 0.7853982 x bore2 x stroke (plug in DST for stroke here to calculate DCR)
Cylinder volume for Dynamic Compression ratio = 0.7853982 x bore2 x DST
Clearance volume = 0.7853982 x bore2 x deck height
Piston dome or dish in cubic inches = cc's x 0.0610237 (- for a dome + for a dish)
Head-gasket volume = 0.7853982 x gasket bore2 x compressed thickness
Chamber volume in inches = cc's x 0.0610237


Displacement = Cylinder Volume * Number of Cylinders
Compression Ration = Cylinder vol. + clearance vol. + piston Comp. vol. + gasket vol. + chamber vol. divided by Clearance vol. + piston vol. + gasket vol. + chamber vol.
Dynamic Compression Ration = Cylinder vol. + clearance vol. + piston Comp. vol. + gasket vol. + chamber vol. divided by Clearance vol. + piston vol. + gasket vol. + chamber vol.

Piston Speed= Stroke x rpm/6



Header pipe length (in inches) = ((850*(360-EVO))/RPM – 3
Header diameter (in inches) = ((cylinder. disp. * 16.38 / ((hdr len + 3) * 25))) * 2.1

These formulas are from A. Graham Bell’s Performance Tuning in Theory and Practice. For a street engine, the RPM used should be the peak torque RPM. For a race engine, the peak hp RPM should be used.

Optimum runner length:

We must take into account the intake duration, but you want the pressure waves to arrive before the valve closes and after it opens (air wont pass though a closed valve). To do this you must subtract some duration, typically you take off 20-30° from the advertised duration. 30° works well for most higher rpm solid cammed drag motors.

ECD = Effective Cam Duration
RV = Reflective Value
D = Runner Diameter

Effective cam duration (ECD) = 720 - (Adv. duration - 30)
optimum intake runner length (L) is:L = ((ECD × 0.25 × V × 2) ÷ (rpm × RV)) - ½D


Intake Ram Pipe Diameter

The formula to figure out the diameter pipe that should be used is for a given velocity is:

D = Square Root of (CID × VE × RPM) ÷ ( V × 1130)

Where:
D = Pipe Diameter
CID = Cubic Inch Displacement
VE = Volumetric Efficiency
V = Velocity in ft/sec

If you're dealing with liters, change CID to liters and the constant to 18.5 so the formula will look like this:

D = Square Root of (Liters × VE × RPM) ÷ (V × 18.5)



Thanks for any replys...

[maxracesoftware]

thanks for the Formulas !!

i have a "Formula" webpage in my Tech Article Section on my Website..but its been empty for awhile...will eventually fill this Page up with a ton of Formulas and source code

since i Program as a Hobby . i've learned its much better/quicker execution to code like this

should be ;
Piston Speed= Stroke x rpm x .1666666667
or
Piston Speed= Stroke * rpm * .1666666667
(do away with division as much as possible)


Piston Speed= Stroke x rpm/6



likewise Bore^2 (squared) would be programmed as

Bore x Bore
or
Bore * Bore

[Steve Smith]

I really like this topic! I've been printing and scribbling notes on just about every word Larry's written to us all. I've more than I can understand at this point but I know I'll work thru it in time. I'll be printing this page as well.
Let's see...I'm forty nine now so if I study continuosly from now on I'll be able to absorb about a quarter of what I read on here...fair enough!

[J-Rod]

Yes, I posted a few I had gather from around, I was hoping Larry, Darin, or anyone else can help by adding a bit. That'd be great....

[maxracesoftware]

another quick "BallPark" Formula ...to calculate what exhaust valve OD would be if you were maxing out the size of the Intake valve OD

Exhaust_Valve_OD = ( Bore * .9211 ) - Intake_Valve_OD

then you would try to place the Exhaust valve over to within .050" of Cylinder wall to unshroud the Intake valve as much as possible.
Then just use Cam specs to spread Centers and design exh port
to makeup for moving Exh valve that close to wall.

example=>

1.802 = ( 4.687 * .9211 ) - 2.515

1.605 = ( 4.185 * .9211 ) - 2.250

1.625 = ( 4.185 * .9211 ) - 2.230


For any number of Cylinders

RPM_Range = ( Cyl_Head_Flow@28" * Cylinders * 1022 ) / CID

Flow_@28" = ( CID * RPM * .000978474 ) / Number_of_Cylinders

[John Wallace]

Larry, these 2 equations:
RPM_Range = ( Cyl_Head_Flow@28" * Cylinders * 1022 ) / CID

Flow_@28" = ( CID * RPM * .000978474 ) / Number_of_Cylinders

Is that the probable 'choke' rpm for that CID and Head flow on the first one and minimum flow for the RPM and CID for the second equation?

[maxracesoftware]

Larry, these 2 equations:
RPM_Range = ( Cyl_Head_Flow@28" * Cylinders * 1022 ) / CID

Flow_@28" = ( CID * RPM * .000978474 ) / Number_of_Cylinders

Is that the probable 'choke' rpm for that CID and Head flow on the first one and minimum flow for the RPM and CID for the second equation?

Sorry i forgot to include the effects of Volumetric Efficiency %
upon that Formula


Flow_@28" = ( CID * RPM * .000978474 ) / Number_of_Cylinders
this Formula calcultes the "most" Flow needed @ 28" on a FlowBench ,
in order to have a chance at making up to 127.5 % Ve

the Formula should instead be =>

Flow = ( CID * RPM * .000978474 * Ve% ) / ( Cylinders * 127.5 )

where
Cylinders = Number of Cylinders
127.5 % Ve = theoretical VE possible at .60 Mach or 699-700 fps
Note=> that 127.5 theoretical Ve is also dependent upon piston speed
and that at lower piston speeds even if there is .60 Mach, its not possible to achieve 127.5 %, but much less

Example=
250.8 CFM @ 28" = ( 362.6 * 7200 * .000978474 * 100 ) / ( 8 * 127.5 )

this shows that the "minimum" amount of Flow @ 28" needed to attain
a Peak HP RPM point at 7200 RPM = 250.8 CFM at 100.0 % Ve

then again you could view that Formula the other way, that is, what's the required Flow @ 28" in order to achieve theoretical 127.5 % Percent Ve
at 7200 rpm ??

319.3 CFM @ 28" = ( 362.6 * 7200 * .000978474 * 127.5 ) / ( 8 * 127.5 )

------------------------------------------------------------------------------------

RPM_Range = ( Cyl_Head_Flow@28" * Cylinders * 1022 ) / CID

this Formula also needs to be changed to =>

RPM = ( Flow * Cylinders * 127.5 ) / ( CID * Ve% * .000978474 )

example=>
7210 RPM = ( 250.8 * 8 * 127.5 ) / ( 362.6 * 100 * .000978474 )

or

7200 RPM = ( 319.3 * 8 * 127.5 ) / ( 362.6 * 127.5 * .000978474 )

or you could view this like whats the possible RPM range Peak HP
would occur at if you varied the Ve ?

9180 RPM = ( 319.3 * 8 * 127.5 ) / ( 362.6 * 100 * .000978474 )

so the minimum RPM point of Peak HP that 319.3 CFM@28" would be
equals 7200 RPM, and the highest RPM point of Peak HP that could be attained with 319.3 cfm on 362.6 cid would be 9180 RPM

i know the results of that Formula looks weired
but it might help if you looked at this way =>
at 7200 RPM with 319.3 cfm and 127.5 Ve,
that 127.5 Ve would also be result of correct cross-sectional area

where as , attaining Peak HP RPM of 9180 with only 100.0 Ve and same
319.3 cfm would be result of very large cross-sect area Cyl Head only flowing 319.3 cfm attaining 100 Ve but still achieving 9180 RPM
...this would tend to be unlikely due to increased pumping/friction losses in real world

[John Wallace]

Thanks Larry.

[ibmorjamn]

just want to bring this to the top so I can find it again. very good archive of info.
it helps with terms and math form as well.
thanks !

[beth]

I like this site. It has many great formulas but they are in calculators so you just plug in the numbers and it does all the work.

http://users.erols.com/srweiss/index.html#jcalc





edited to correct wording