DUDE!!!!! Welcome back!!

 

Thanks for that guys. I've settled into a new line of work(Industrial Design/Product Development and Engineering) after spending a bit of time in motorsport as a fabricator/designer for bespoke parts. I've sold the Evo and will be starting a new project mid year. It will be my first ground-up vehicle design, so I am trying to get my head around the kinematics side of things early on.

My new job isn't as interesting, but the pay is better and my boss is also a car nut(though he's into the Euro's.)

But anyhoo back on topic, the tyre represents perhaps the greatest loss aside from the inherent flex in all the bits. A low profile tyre on a small rim(one that will of course clear the calipers and discs) will help quite a bit, as the sidewall needs to be targeted specifically. The tread pattern also needs to be addressed as you should want to have no slip on the dyno. THIS is the hard bit as it means you want the best tyre to spin the retarder/roller with. Unfortunately, the best tyre to do that with seems to be a 10-year old tyre that has been in the sun all that time(read:dead material) with just enough tread to find purchase. This is the compromise in order to reach the goal: the tyre works well on the dyno, but it will NOT work well on the road: to generate its grip, a good deal of energy must be used and heat must be generated between the tyre and the road in accordance to the range the manufacturer has designed the tyre to. The rim also plays a part, and so do all the elastomeric bits and pieces in the body(which also eat up the energy) but the choice of the driving tyres are usually the biggest culprit in this discrepancy.

As a rule of thumb, look at the vehicle as a whole. Wherever heat is being generated per given unit time, and where large amounts of lubrication are needed, is where you are losing energy(all the way to distortion in the block and head)

 

^^ You say a low profile tire. For most people that means a bigger rim. Bigger rims mean more weight which has more rotational mass which in turn loses more power. When the of the pneumatic suspension system and the rubber of the tire weigh less per inch then the rim, it might make more sense to pick the lesser of the two evils. To my mind, it seems that the rubber and the pneumatics would resist change of speed, but only when the rotational force is first applied and from then out, its like dealing with a coiled spring. The rotational mass, weight of the rim, on the other hand is a constant force working against you.
So while decreasing the pneumatic/rubber suspension system on the tire would make it more firm and transfer more immediate power to the ground, a heavier rim would be counterproductive. At the same time, if you go too low on the tire's profile, it will not have enough of it's pneumatic suspension system to keep contact with the ground and therefore will spin rather then grip because of the lessened contact surface and the tire's inability to flex around small rocks.

There must be some sort of calculation to tell you where the optimum rim size would be.

 

A low-sidewall(profile) tyre, on a small rim. Yes, this does mean that the OD of the wheel package will in all likelihood be reduced. As long as it clears the brakes. Looks are irrelevant to the exercise. The OP wants to reduce the difference between the figure shown on an engine dyno, and and the figure shown at the rollers. He said that "this is the only thing that matters," and so we throw grip and feel out the window for just this exercise(where, in the real world, these are more important than wheel hp)

Small rim, low profile tyre that will allow only minimal sidewall flex. As a byproduct, also reducing rotational inertia that has to be overcome.

And that is only part of the story. The last part. Everything in between also has to be looked at in order for energy losses to be contained. In a production car with production bits, you can be assured that almost nothing in it, is going to be as stiff as it can be.