Valves - Exhaust - Speed - Airflow - Graphs - Cooling - Springs - Tyres - Nacaduct
written by Rienk Steenhuis
valves.xls (20kb, Excel 97)
Here follows the list of data as I copied it from a 60s tuning book. I think it was called "Tuning Four Stroke Engines". Unfortunately, I didn't copy the title or the writer's name.
|port to valve ratio (inlet)||inlet to exhaust valve ratio|
|= 0.81 - 0.83 to 1
= 0.72 - 0.73 to 1
= 0.75 - 0.76 to 1
|1 to 0.65 - 0.68 for road - rally|
1 to 0.70 - 0.73 for race
|port to valve ratio (exhaust) = 0.95 - 1 to 1|
|equation: RPM = Gs x 5600 x Va / Cv||Gs = gasspeed at inlet valve in F/s|
Va = valve area in Square inch
Cv = cylinder volume in cc
All the ratios are area and not diameter.
The gasspeed table is in the spread sheet and so is the valve size table. I therefore didn't copy it here. The valve sizes are optimal for an engine producing maximum bhp at 7000 - 8000 rpm.
There are two problems with the equation : the definition of valve area and the number 5600. I have taken valve area to mean the circumference of the valve x the lift. This may of course be wrong. Some of the rpm that come out of the equation are clearly of by a big margin. I'm trying to determine where things go wrong.
Working the equation so it is in metric units :
|RPS = Gs x 0.475 x Va / Cv||Gs in m/s|
Va in m²
Cv in m³
This can also be written as : 2.107 x Cv x RPS = Gs x Va = pumped volume per second.
Why the number should be 2.107 instead of the expected 2 I cannot say. After all it suggests a volumetric efficiency of 105 % at maximum revs. It may be that in combination with his list of estimated gasspeeds this gets the best results. For now I've left it as it is but I do realize that results are only approximate and I may have to adjust later.
exhaust.xls (19kb, Excel 97)
Headers, downpipes and tailpipe are called primary, secondary and end pipes respectively. I don't know whether this is British versus American.
Exhaust gas velocity is given as 200 - 300 F/s and pressure wave velocity as 1500 - 1700 F/s. The one thing that wasn't mentioned is that the velocities drop further away from the valve. This as a result of changing temperature and different pipe diameters.
length of primary = (850 x EO / tuned RPM) - 3where EO = exhaust open bbdc + 180 degrees. This then results in a length in inches. The number 3 is most likely the length of the port in the cylinderhead. Since the length of exhaust wil be twice the length from the valve to the joint, the length of the primary is ¼ of the distance traveled by the pressure wave. the equation can be re written as :
bbdc + 180 / 360
|12 converts to inches, |
60 to RPS and
4 x RPM x 360 gives the part of the circel between bbdc and tdc.
The difficult bits here are the diameters of the pipes.
|ID1 = 2.1 x sqr (Cv / (25 x P))
ID2 = 0.93 x sqr (2 x ID1²)
ID3 = 2 x sqr ((2 x Cv) / (25 x P))
|P is the length of the primary pipe + 3
Cv is cylinder volume in cc
Clearly the diameter depends on the cylinder volume and on the length of the pipe. If Cv is measured in cubic inch then the number 25 would change to 1.526 which doesn't clarify anything for me.
Rereading Willy Griffiths advice on the exhaust system it is evident that he uses a different way to determine the lengths. His primaries are 13 inch and 1 1/8 diameter secondaries are 9 - 10 inch and 1 3/8 tailpipe is 30 inch and 1 1/2. secondaries are shortened to 5 - 6 inch for racing. This means 22 -23 inches to where the tailpipe starts or 18 -19 inches for racing. Tim Millington gives the lengths as at least 12 inch primaries and 35 to 40 inches to the tailpipe for a road car and 27 to 30 inches for racing. His tailpipe is 30 inch and not critical. I've measured the imp sport system and it is approx. 30 inch to the silencer. This is what my spread sheet comes up with as well. The Janspeed big-bore system is approx. 28 inches to the joint. with 9 inches for the primaries.
There is a book called "The Scientific Design of Exhaust and Intake Systems" by Philip H. Smith. His work used to apear in C.C.C magazine.
speed.xls (18kb, Excel 97)
The general equation for calculating the energy involved in attaining a certain speed is:
|P= ½ x rho x FA x V³||P in joules|
FA in square metres
V in m/s
airflow.xls (18kb, Excel 97)
This is a spread sheet which I set up to juggle a variety of unknowns. The values of 33 Mj/litre and the equation linking air density to temperature I got from a physics book that is commonly used in Dutch schools. It holds equations for maths, physics and chemistry. The figures for gasspeed in the port or at the valve are very different from the ones in the valve spread sheet. The number of 34% for the thermal efficiency is the one that Gary told me at National day (which might have been called international day of course). The figure generally given in environmental publications is 25%. I don't know if they mean gross or netto or wether camshaft and oil and waterpump are included.
The three camshafts I've measured myself. I started on this in fact because I didn't know what the cam in Franka's car was. There are no markings on it. So me calling it a R17 is because it looks like one.
|red = exhaust lift
blue = exhaust speed
brown = exhaust accelleration
|black = inlet lift
green = inlet speed
purple = inlet accelleration
in 0.01 mm/deg
in 0.01 mm / deg /deg
The safe tappet velocity for the imp as given by the 60 tuning book mentioned earlier is 9.35 thou inch or 0.2375 mm all camshafts stay well within that limit. The velocity seems to be limited by the tappet diameter.
A dutch car magazine article gave me the data for the standard imp power output. Their figures are extremely low. But the car still managed a 128 km (79.5 mph) topspeed. This means either their rolling road was of the mark by a long stretch or Rootes power figures were very optimistic. If the engine output as measured was correct then the resulting CD factor would have been a very flattering 0.348.
Once again I had to enter the lions cage so to speak. This is of course the reason for all the different ways of calculation. The starting point for me was the assumption that the same amount that goes to the flywheel has to go to the cooling system as well and that the cooling system just acts as an intermediary between the engine and the surrounding air. Furthermore I took the power figures for the fan as given by Tim Millington as essentially correct. The equation for the energy that is contained in a certain volume of air moving at a certain speed I found in a book about windmills.
equation : P=1/2 x rho x area x V³ x 16/27
equation : P=1/2 x rho x area xV³ X 27/16
or : V= ((P x 16/27) / (0.5 x rho x area))^ 1/3
This spread sheet is based upon chapter 8 of the book "Competition Car Suspension" by Allan Staniforth. The chapter was written by David Gould. The values that I entered in the equations are not necessarily correct. Things like track and roll centre height depend very much on the ride height of the car. The same applies to to suspension leverage versus camber. On a swingaxle suspension like the Imp the roll centre is at nearly the same height as the pivot points. At the rear you first need to determine the length of the imaginary swingaxle that would move the wheel through the same arc. This length can be derived from page 24 section F of the Chrysler Workshop Manual. This gives the dimension between the pivot points as 218.44 mm. Drawings like these are usually to scale, so from the centre line of the drive shaft to the intersectionpoint with the line through the pivots is
218.44 x 100.7 / 70.7 = 409.6 mm(100.7 and 70.7 measured from page). From this the intersection from the line through the drive shaft and pivot points can be calculated with the sine rule : a/sin a = b/sin b = c/sin b
409.6 x sin 16/ sin 74 = 1428 mm or 56.22 inches
To this you need to add the distance from the rear of the brake backplate to the centre of the tyre contact patch which of course once again depends on the sort of wheel tyre combination and camber angle you are using. Anything from 0.5 to 2 inches is possible. Changing the perspective and looking from the back you can now imagine three lines:
For the engine compartment and the front boot similar guesstimates can be made. As to the spring rate and the fitted rates, once again these are as accurate as I can make out. But the move ratio (the amount the spring moves with respect to the tyre patch) depends on the track which in turn depends on the wheel -tyre combination and the camber. And then you still have to believe the spring rate as given by Rootes which I believe to be somewhat suspect. The best thing is to go out and measure your own car as accurately as possible. The figures as I put them in are what I believed them to be at that moment.
This is based on the articles by Paul Wiliams and Martyn Morgan Jones in Impressions. It can only be used as a general guide line. The details as given by the manufacturers take precedence of course. And they have their own reasons for doing things over which we have no say at all. Enough said.
nacaduct.xls (23kb, Excel 97)
Enables you to design a nacaduct. Based on work from the Royal Aeronautical Society and a mister C. Smith. They give slightly different shapes. I don't know which is best. The idea behind this type of duct is to get air through a panel whithout disturbing the flow over that panel. It tries to accomplish this by creating a controlled vortex at the sides of the ramp. This in turn keeps the airflow close to the bottom of the ramp. The lip at the end is supposed to be the front of a wing section. On a vulcan bomber it isn't there. This makes the space needed much smaller.
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