Ok, one final post to finish up our work on modelling.
The next task we can use our model for is to work out how specific superchargers will behave on our grey motor. A larger supercharger will not need to spin as fast as a smaller supercharger to achieve the same boost pressure. Also, if we have a given supercharger we can change the crank (or drive) pulley to spin it faster or slower, achieving different boost pressures with the same machine.
The calculation process is as follows. Note that I will continue on using the data from the example above.
1. We start by determining the airflow through the engine without the supercharger:
Naturally aspirated engine airflow = (engine capacity x rpm x 0.5 x volumetric efficiency)/1728
For our example grey motor, the engine capacity is 138ci, our redline speed is 4200rpm and our engine volumetric efficiency is 80%. This gives:
Naturally aspirated engine airflow = (138x4200x0.5x0.
/1728 = 134cfm.
2. We can then calculate the (now pressurised) air flow required by the supercharged engine:
Supercharged air flow rate = basic engine flow rate x pressure ratio
If we look at the point where our supercharged grey motor was making 110BHP, boost was 12.9psi and the pressure ratio was 1.47. This gives:
Supercharged air flow rate = 134 x 1.47 = 252cfm.
3. Next we can calculate how fast a given supercharger will need to spin to deliver this flow.
Supercharger speed = (supercharged air flow x 1728)/supercharger capacity
If we assume that we are supercharging with my small Norman (83ci/rev capacity), then:
Supercharger speed = (252 x 1728)/83 = 5260rpm.
This shows that whilst our engine is turning at 4200rpm, our supercharger will need to be turned somewhat faster (overdriven) in order to achieve the boost pressure (and hence power) we are seeking. This seems a little odd, as most Normans are driven at pretty close to engine speed. The reason for this is that the example above has no water injection, and hence the gases exiting the supercharger are hot and not very dense. If we cool them by water injection, then we get results closer to engine speed (see graph and discussion below).
4. To overdrive the supercharger, we can change either the drive (crankshaft) pulley, or the driven (supercharger) pulley size. Making the crank pulley smaller will underdrive (slow) the supercharger, whilst making the supercharger pulley smaller will overdrive (speed up) the supercharger. To determine the relative sizes of the two pulley we need:
Crank pulley ratio = supercharger speed/engine redline
For our example, this gives:
Crank pulley ratio = 5260/4200 = 1.253
This means that we would need to have a crank pulley that is 25% larger in diameter than the supercharger pulley. As an example, if we assume that we have something similar to the factory FE-EJ Holden grey motor harmonic balancer on the end of the crank, our crank pulley diameter is 45/8”. This would require a supercharger pulley of 45/8/1.253 = 3.69” diameter.
Using the above calculation process means that for a given engine and supercharger we can work out how it will behave for a given pulley size. As examples, if we use our example grey motor from above but this time adding water injection to achieve a 50ºC supercharger outlet temperature, we can plot the following chart for different superchargers:
From the above, we can see that different superchargers can be used to get the same power output on our grey motor, but will spin at different speeds. For example, at 120BHP output Harv’s small Norman will be spinning at more than twice the speed than if we had of bolted on Gary’s large Norman. From the above, we can see that a given Norman supercharger has:
a) A capacity – it will push out a given amount of air every time the shaft is turned, and
b) A point of maximum efficiency – it runs “happiest” at a given pressure.
c) We can get more boost out of a given supercharger by spinning it faster.
However, a word of caution here. Although a larger supercharger can be used and turned slower (within reason), the inverse is not always true (i.e. you cannot always take a too-small supercharger and spin the crap out of it to get the right boost). This is because at high speeds:
a) the amount of air slipping past the vanes and being churned up inside the supercharger increases,
b) less time is available for the air to flow backwards and forwards when discharging (if we are not at the point of maximum efficiency (or “happiest” pressure),
c) the superchargers ability to suck in and blow out each parcel of air begins to be constrained by the inlet and discharge port geometry.
d) more power is taken up driving the supercharger itself.
In the end, this becomes a case of diminishing returns – we get less and less additional boost despite spinning the supercharger faster and faster. Whilst every application of a Norman will vary, practical guidance (Go for Blow, 2009 Street Machine Hot Rod Annual) indicates that 6-7psi is a typical point of diminishing returns for early Normans.
We can also plot out pulley ratio for each of our example superchargers:
This shows that for Harv’s small Norman and a pulley ratio of 1:1 we would get about 115BHP.
Finally, for a given supercharger we can see how it will perform for a given range of pulleys. For example, for Harv’s small Norman if we assume we are running a crank pulley similar to the standard FE-EJ Holden (45/8” diameter), then the supercharger would behave as follows:
This shows that for our target 50% power increase to 110BHP we would be looking for a supercharger pulley diameter similar to that on the crank, and would be running at around 8psi (with our water injection holding discharge temperature to 50ºC). These numbers line up pretty well with the anecdotes from old Norman operation.
Cheers,
Harv (deputy apprentice Norman fiddler).
327 Chev EK wagon, original EK ute for Number 1 Daughter, an FB sedan meth monster project and a BB/MD grey motored FED.