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Help on flow math

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Help on flow math

Postby dougk » Mon Jan 24, 2005 8:44 pm

I'm trying to reconcile a couple of formulas to figure port flow in fps.
I'm porting my Ducati's 2 valve heads and trying to figure out flow speeds in various parts of the port. Unlike car engines the port is a diffuser ie: it increases in diameter from the port flange in, except for the obstruction of the valve guide. The port flange is even smaller than the throat of the seat.

The formula I've been using I got from Kevin Cameron's book "Sport Bike Performance Handbook" as follows:
Take the ratio of the port dia to bore dia and square that. Multiply that by the piston speed in ft per second. This gives average velocity. Plugging in some numbers:
(bore) 3.622/ 1.34 (port dia) = 2.70
Square that = 7.31
Piston speed at max. torque in fps. = 40.898
40.898 * 7.31 =298.96 fps a not unreasonable port speed.

Now using the equation from the Mach .55 Hp flow loss :
FPS = ( bore * bore * stroke * rpm * .00353 )/ ca
ca = port area
ca = 1.41 sq in ( 1.34 * 1.34 * .7854)
stroke = 2.677
piston speed at max torque ( 5500 rpm) = 2454 fpm
Plugging in the numbers:
FPS = ( 3.622 *3.622 * 2.677 * 5500 * .00353) / 1.41 = 483.57

Since as I understand it, well developed race engines ie. Pro Stock, Formula 1 are getting 400 + fps, I find it hard to believe a stock Ducati port is flowing at 483 fps.
Can somebody help me tie these two formulas together or do I just pick one and plug in the various dimentions from my port and just look at the relative numbers?

Thanks for all the great info on this board, I read it daily!
dougk
 

Postby maxracesoftware » Mon Jan 24, 2005 11:07 pm

Now using the equation from the Mach .55 Hp flow loss :
FPS = ( bore * bore * stroke * rpm * .00353 )/ ca
ca = port area
ca = 1.41 sq in ( 1.34 * 1.34 * .7854)
stroke = 2.677
piston speed at max torque ( 5500 rpm) = 2454 fpm
Plugging in the numbers:
FPS = ( 3.622 *3.622 * 2.677 * 5500 * .00353) / 1.41 = 483.57


the above Formula is used to give a person an idea
at what RPM or minimum cross-sectional area ,
an Engine will be "Choked" at .

your 483.57 fps is less than the theoretical .55 Mach limit,
but this is occuring at the RPM point of Peak Torque.
So at 5500 RPM the velocity thru the smallest cross-sectional area
is OK...this is not Choked ! , but the Formula should have
the RPM point of Peak HP inputed instead of the RPM point of
Peak Torque.


your Engine is probably making its Peak HP at 7000 RPM
or falling off after 7000 RPM, and near 7000 RPM and above
the Formula predicts your engine will be theoretically "Choked" .

615.46 fps = ( 3.622 * 3.622 * 2.677 * 7000 * .00353 ) / 1.41

.5515 Mach = 615.46 fps / 1116 fps


also ...
it is possible to achieve .627 Mach (700 FPS) or slightly higher
with very good Port design

.627 Mach = 127.5 % PerCent Volumetric Efficiency potential

.55 MACH = 121.1 % PerCent Ve
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Postby maxracesoftware » Mon Jan 24, 2005 11:26 pm

I'm trying to reconcile a couple of formulas to figure port flow in fps.
I'm porting my Ducati's 2 valve heads and trying to figure out flow speeds in various parts of the port.


to get an idea of velocity in feet per second, in various parts of a Port,
then you would need to Flow Test Heads on a FlowBench
then measure the various cross-sectional areas you're interested in
and use the Formulas below to give you an idea/guesstimate.

FPS = ( CFM / CA ) * 2.4

CFM = FPS * CA * .41666667

CA = ( CFM / FPS ) * 2.4


but be careful...to get the "real velocity fps" , you must use a
Pitot Probe while Flow testing the Head....as the actual shape
of the Port's walls can greatly change actual local velocity
-VS- the theoretical velocity calculated by the above Formulas.

its very possible for a Port to be Choked "before"
what the above Formula predicts

there can also be spots of localized velocity that will cause
Air/Fuel separation or Choke

you never want your Pitot Probe pressure reading to equal or exceed
your Flow Test Pressure....sometimes you can get away with that much velocity at the Short Turn Apex....but you can almost never get away with that much velocity further up the Port or a greater distance away from the Short Turn.


if your Pitot Probe Pressure >= Flow Test Pressure
then it will equate to Choked velocity in a live engine
at a certain Piston speed .
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Postby maxracesoftware » Mon Jan 24, 2005 11:42 pm

The formula I've been using I got from Kevin Cameron's book "Sport Bike Performance Handbook" as follows:
Take the ratio of the port dia to bore dia and square that. Multiply that by the piston speed in ft per second. This gives average velocity. Plugging in some numbers:
(bore) 3.622/ 1.34 (port dia) = 2.70
Square that = 7.31
Piston speed at max. torque in fps. = 40.898
40.898 * 7.31 =298.96 fps a not unreasonable port speed.


Lets use the above Formula in the
"Sport Bike Performance Handbook"
for an Engine like a ProStocker 500 cid at 9000 RPM

Bore = 4.687
Stroke = 3.620
Piston Speed FPS = ( 3.620 * .16666667 * 9000 ) / 60 seconds

Piston Speed FPS = 90.49999 fps

Minimum Cross-sectional area = 4.115 square inches

FPS = (( 4.687 / 4.115 ) ^ 2 ) * 90.49999
FPS = 117.408 fps

117.408 FPS at 9000 RPM seems very low
are you sure you copied the above Formula
from the "Sport Bike Performance Handbook" correctly ??

it seemed close for your application,
but its a mile off for a ProStocker !!
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math

Postby dougk » Tue Jan 25, 2005 1:35 am

Thanks Larry.. how about 379.4534 fps. I think it's based on diameters. If you figure what sized circle = 4.115 sq in , it comes out to 2.228969359 dia.
A lot of numbers after the decimal, but you need them to get 4.115.

4.687/ 2.228969359 = 2.047646458

2.047646458 ^2 = 4.1928560

4.1928560 * 90.49999 = 379.4534275 fps

Does that sound more realistic?

You're right, the engine peaked at 7000 and that probably explaines why
the last 3 lifts remained flat on the flow bench - .350-.400-.450". Valve lift is .460".I do have a bench I built to do this. I have made a U shaped probe but it's not a pitot. Does the static input of the pitot have to be at the very end?

There also had to be some intake length tuning going on also because those figures were with the original 7" intakes. When I went to about 2 3/4
in long intakes torque went up to 6500 and hp at 8500. Power was up 8%
dougk
 

Postby maxracesoftware » Tue Jan 25, 2005 2:13 am

Thanks Larry.. how about 379.4534 fps. I think it's based on diameters. If you figure what sized circle = 4.115 sq in , it comes out to 2.228969359 dia.
A lot of numbers after the decimal, but you need them to get 4.115.

4.687/ 2.228969359 = 2.047646458

2.047646458 ^2 = 4.1928560

4.1928560 * 90.49999 = 379.4534275 fps

Does that sound more realistic?



yes .... sounds closer :)

the Formula in the "Sport Bike Performance Handbook"
is just the old average or mean gas velocity formula though a Port in FPS

FPS = ((Bore_Dia ^2) / (Port_Dia ^2)) * (( RPM * Stroke * .16667) / 60)

Equivalent_Port_Diameter =( CA * 1.273239545 ) ^ .5

where;
CA = minimum cross-sectional area in square inches
1.273239545 = Constant = 1 / .785398163
.785398163 = Pi or 3.141592654 / 4

Min_Cross-Sectional Area = 4.115 sq.in.
Port_Diameter = ( 4.115 * 1.273239545 ) ^.5
Port_Diameter = 2.28897 inches

FPS = ((Bore_Dia ^2) / (Port_Dia ^2)) * (( RPM * Stroke * .16667) / 60)

379.4611 fps = ( 21.967969 / 5.239380728 ) * ( ( 9000*3.620*.16667 ) / 60 )
Last edited by maxracesoftware on Tue Jan 25, 2005 2:51 am, edited 1 time in total.
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Postby maxracesoftware » Tue Jan 25, 2005 2:28 am

You're right, the engine peaked at 7000 and that probably explaines why
the last 3 lifts remained flat on the flow bench - .350-.400-.450". Valve lift is .460".I do have a bench I built to do this. I have made a U shaped probe but it's not a pitot. Does the static input of the pitot have to be at the very end?


even if your last 3 Valve Lift points in a FlowBench test
were steadily increasing, the Engine should still be
theoretically choked by the prediction of the .55 Mach Formula
or close to that prediction.

in other words... a Live Engine Choke problem will not show up
in a FlowBench test just looking at Flow numbers to whether they
are increasing, leaveling off, or decreasing.
The Heads can have great Flow numbers , but on a live Engine,
be severly Choked ,....you need to atleast calculate FPS by measuring various Port areas...but the best way, is to measure Port velocities with a commercial made Pitot Tube 180 deg bend for Intake Ports

i would purchase either a SuperFlow, Dwyer, or Performance Trends
Pitot Probe.

it will be hard for you to make a Tube within a Tube,
drill all the tiny Static Pressure sensing holes,
bend the Tube within a Tube into a smooth radius,
and shape the leading edge of the Probe and velocity measuring orifice properly to an aerodynamic radius.

Probes will be cheap considering the time and effort you spend to duplicate a commercial made Probe.

Also there are stainless-steel Pitot Probes with etched or indented marks
every 1/2 inch to be used as depth referrence...you could do the same with any Pitot Probe by just marking with a Scribe or Mark-A-Lot or Sharpie
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Postby maxracesoftware » Tue Jan 25, 2005 3:31 am

Can somebody help me tie these two formulas together


dougk .... here's more Math you might be interested in ????

in the above comparisons between the Ducati MotorCycle and the ProStocker ....calculations are =>

using the Formula in the "Sport Bike Performance Handbook"
FPS = ((Bore_Dia ^2) / (Port_Dia ^2)) * (( RPM * Stroke * .16667) / 60)


ProStocker 500 cid at 9000 RPMs = 379.4534275 fps

Ducati at 7000 RPMs= 380.3118796 fps

where;
bore= 3.622
stroke = 2.677
port dia = 1.34
piston speed at 7000 RPM = 52.053 fps


379.4534275 fps -VS- 380.3118796 fps ...very, very, close :)


"CHOKE" or port limiting velocity is occuring when
Pitot Probe pressure >= Flow Test Pressure
"relative" to a live running Engine at a certain Piston Speed :)

"CHOKE" can occur sooner or later than 28" Probe Pressure when flow testing at 28" inches,...just depends on shape !! or localized velocities
..and most importantly..is where in the Port are you measuring Pressure/Velocity...and at what Valve Lift is the most important ??

obviously...you want a Port Shape to "extend" the RPM point of CHOKE
just think of the HP if you could make a Port a straight tube ??
and/or reach 1.00 MACH ??? :shock:
Last edited by maxracesoftware on Thu Jan 27, 2005 10:30 am, edited 1 time in total.
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Postby dougk » Tue Jan 25, 2005 12:56 pm

Thanks Larry.....I was kinda stuck, now I've got the info to proceed. :D
dougk
 

Postby dougk » Tue Jan 25, 2005 1:13 pm

I forgot to ask.... what is the math for mach number to theoretical VE?
dougk
 

Postby maxracesoftware » Tue Jan 25, 2005 1:55 pm

I forgot to ask.... what is the math for mach number to theoretical VE?


don't ask ... its a SECRET . :)

a little more Flow Math / Equations =>

the Formula in the "Sport Bike Performance Handbook"
FPS = ((Bore_Dia ^2) / (Port_Dia ^2)) * (( RPM * Stroke * .16667) / 60)

can also be found in the back of Philip H Smith's Book
"Scientific Design of Exhaust and Intake Systems"
===============================================



you can use the "below" Formula to solve for
Seat Insert Diameter / Throat Diameter / or Valve Diameter

CA = ( Bore * Bore * Stroke * RPM * .00353 ) / 614

Equivalent_Port_Diameter =( CA * 1.273239545 ) ^ .5

Example=> ProStock

4.1148 = ( 4.687 * 4.687 * 3.620 * 9000 * .00353 ) / 614

2.288910018 =( 4.1148 * 1.273239545 ) ^ .5

.910103387 = 2.288910018 / 2.515 Intake Valve OD
91 PerCent throat or seat diameter of the Intake Valve diameter
close to Darin Morgan's 90 % Rule

Intake_Valve_OD = Equivalent_Port_Dia / .90 to .91 PerCent Rule


another example => NHRA SS/IA 350 SuperStocker w/ 1.940 Int OD

2.389233064 = ( 4.065 * 4.065 * 3.493 * 7200 * .00353 ) / 614
1.744151948 = ( 2.389233064 * 1.273239545 ) ^ .5

1.74415198 / 1.940 Intake Valve OD = .89905 PerCent
again close to Darin's 90 % PerCent Rule :)

try it with Ducati 2-Valve and see what you get ??
might be interesting ??
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Postby SteveS » Tue Jan 25, 2005 8:56 pm

Larry
Interesting reconciliation of different calculations. How accurate is the data generated through this link:
http://www.wallaceracing.com/machcalc.php

And how do reconcile the calculation of mach indexes using valve diameters and lift, on the one hand and as is done in the above link, and cross sectional area, as you have explained, on the other?
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Postby dougk » Tue Jan 25, 2005 9:31 pm

Sorry, didn't realise VE was one of those questions. :D

I haven't figured what my throat dia should be using flow velocity but I think I originally measured 87%. I am playing with a spare head and it's at 94% now.To big, I know. I've read more than one place 85% so I'm going to reread all the porting posts to see why it's gotten pushed to the 90% region.

I think my port flange is going to be my choke point as it's smaller than the throat. Not sure what to do about that yet. I sucessfully made a pitot probe today with an 1/8" OD, so I should be probing shortly.

What are some typical HP/Torque numbers for ProStock?
dougk
 

Postby maxracesoftware » Wed Jan 26, 2005 2:40 pm

Larry
Interesting reconciliation of different calculations. How accurate is the data generated through this link:
http://www.wallaceracing.com/machcalc.php


its pretty close .... but seems to calculate Mach number
too low by approx. .095867 Mach on average,
and the correlation is not as accurate as the Formula below

FPS = ( Bore * Bore * Stroke * RPM * .00353 ) / Cross-Sectional Area

then
Mach Number = FPS / 1116


And how do reconcile the calculation of mach indexes using valve diameters and lift, on the one hand and as is done in the above link, and cross sectional area, as you have explained, on the other?


where ever the smallest cross-sectional area is located
then it will eventually, and ultimately be the "Choke" point

if that Choke-area is at the pushrod, then it will set the Mach number
the Port/Engine will be choked at.

if the Choke area is the Curtain area, then it will set the Mach number
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Postby maxracesoftware » Wed Jan 26, 2005 2:44 pm

Sorry, didn't realise VE was one of those questions.


.627 Mach = 127.5 % PerCent Volumetric Efficiency potential
.55 MACH = 121.1 % PerCent Ve

those values are just the "Ve % potential" -vs- Mach number
and does not included effects of wave tuning

you can make 127 Ve% with .55 MACH
with the additional effects of Wave Tuning
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