Does a short non-driven tire take less power to accelerate than a tall tire.....

[voodooracer]

......to the same vehicle terminal velocity? Terminal speed is 100 mph. Short tire o.d. is 21.5 compared to tall tire o.d. of 27.2 I've calculated tire RPM for the short tire as 1600 vs. 1245 at the same 100 mph. Weight of the short tire is 3.625 lbs vs. 7.0 lbs. for the tall one.
 Thanks in advance to anyone who can help. I've tried various words and phrases (and clauses) in search to no avail.
 I'm changing to a lighter frt end on my dragbike (1/8th mile only) and it would be a good time to gain the rollout advantage of a tall frt. tire, but not if I give it all back by taking longer to get it up to speed as I only have so much distance to work with. Unless it reaches a lower terminal velocity but in a shorter time over the same distance. I also don't want to save 10lbs. on the front end swap and introduce so much more rotational weight that it kills et. Unlike you guys and galls, I'll trade mph for et any day.
 But man, that much rollout! Talk about a head start!
 Keith LeBlanc

[Interested Observer]

To properly determine the answer one would have to know the weights and rotational inertias of the two rotating assemblies--tire/tube/wheel/brakes?/hub etc.  This could be measured as described in the Build Diaries of this board at Milwaukee Midget, page 119 reply 1776 and page 123 reply 1833.  In your case the wheel assembly would replace the rocker arm described there, and since presumably your CG will be at the center of rotation, your quantity “r” would be zero.
Then, calculate the relative kinetic energies of the two at 100 mph.

Eshort/Etall = ratio of translational energy + ratio of rotational energy

If one assumes translational energies are comparable, then Es/Et = (Is/It)*(RPMs/RPMt)^2   where I’s are the rotational inertias measured above and the RPM ratio (which will be squared--the “^2” notation) is as you have determined.  If the finished energy ratio is less than one, the short tire wins--having stored less energy than the tall one.  Conversely, greater than one, the tall setup is better.  (Ignoring aerodynamic differences.)

[Richard 2]

It seems to me if you can push the vehicle by hand easily the wheel height wouldn't matter much on a none driven wheel.  Just a thought.

[Stainless1]

IO has it right... at the very end... the part in parentheses... aero is better on the little tire, less frontal area... the roll out thing?  you get maybe 1-2 inch head start... but you gain weight, I'd go little tire every time.

[voodooracer]

 Thanks for the replies. Got some gazintas to do.
 Keith LeBlanc

[Dean Los Angeles]

The tire answer is about friction.

You have aero friction from the tire and wheel that is significant. It isn't streamlined and it's rotating. Smaller is better.

The contact patch with the ground creates friction. Smaller is better. You don't need much in the way of steering input.

Sidewall flex creates a large amount of friction. High air pressures help here.

The wheel bearing (not part of the tire, but since we are here . . .) can be a source of unwanted friction. If you spin the tire is should go for a long time. Standard bearings have grease and seals. The high dollar answer is to switch to ceramic bearings. Otherwise, remove the seals and replace the grease with light weight oil.

[SPARKY]

The mass of the shorter tire will be easier to spin up and to stop due to the diff of length of the radius moment arm ... I may not be using the terms correctly 

[jimmy six]

No proof but a very knowledgable Land Speed Racer told me in the 70's it easier to pull a gear than it is to pull a tire.......only went to a big tire when I had no choice.....Good Luck.

[tallguy]

Here's my two cents' worth:

The recent response that talked about rotational inertia makes sense to me
(a mechanical engineer).  You may also want to consider, regardless of that,
"pretending", temporarily, that the wheel isn't rotating while you travel at
speed.  Ignoring rotational inertia and rotational acceleration, the lighter
tire will be easier to accelerate in a straight path, say, from a standstill
to any given speed, compared to the heavier tire.  Remember F=ma? 
In addition, the shorter tire may allow the vehicle body to be less tall and
therefore more aerodynamic.

Tallguy