Rotating Mass – Marketing Fallacy?

[Scott McFadden]

Rotating Mass – Marketing Fallacy?

It’s not that I have nothing better to do, but after reading and hearing about the benefits of lower rotational mass, I’ve been giving the concept some thought. My conclusion is simple – given a kart at the minimum weight, lowering rotational mass of kart components makes no difference to performance. Tell me if I'm wrong.

Wait, I’m going to try to support my argument. First we need to make some assumptions:
1. the kart and driver with ballast if necessary is at the minimum weight for the class
2. the kart will go quickest when traction is maintained i.e. no wheel spin
3. we’re relying on one motor with constant power
4. we remain within the reasonable mechanical efficiencies of the various rotating components (drag friction terminal velocity)
5. all rotating components have their axes perpendicular to the direction of travel ie fore and aft
6. for now we’ll deal with straight-line acceleration (acceleration and deceleration can be considered to be the same things given the above assumptions).
7. that those prepared to respond to this post have brushed up on Isaac Newton’s laws of motion

The first thing that needs to be considered, and is very straightforward, is that when a kart accelerates, the factor limiting the rate of acceleration is weight aka “mass.” The lighter you make it the faster it will accelerate and vice versa.

So the question is - does it matter whether the weight is part of rotating or non rotating parts? Lets pick one part that is sort of in-between…..the chain.

Picture if you will, a single link of the chain. No matter which position you put it in by rotating the sprockets, it will basically have an identical link across from it and travelling in the opposite direction.

Now think of that same link as it leaves the engine sprocket. Regardless of the speed the kart is travelling, that link will be stationary relative to the ground (just as the contact patch of the tires is “stuck” to the track). As the kart accelerates our link actually stays still. So it’s mass is effectively invisible to the kart as far as acceleration is concerned.

Trouble is we have its opposite link, which is in fact being accelerated at twice the rate of the kart as it moves the distance between the rear sprocket and the engine sprocket. It therefore has effectively twice the mass relative to the kart. So you can see that the pesky upper link is cancelling out the effective zero mass of the lower link. This happens for every link of the chain at all points in the rotation, forward & back and up& down.

So the lower the rotating mass crowd would have us believe that going to a smaller size chain, will allow the kart to accelerate faster. But if the kart is at minimum weight, ballast must be added, which still has to be accelerated. The lighter links of the chain cancel each other out because for each one accelerating forward there is one stopped.

Moving from the chain to lets say a brake rotor, the principle of the chain is very similar except each “portion” of the rotor is only stopped relative to the track when it is at the bottom of its rotation or “bottom dead centre” (BDC). As any point on the rotor approaches BDC it will be slowing down in relation to the track. It will be stopped at BDC then accelerate to twice the speed of the kart (and therefore twice the rate of acceleration as it moves to top dead centre. So you can drill all the holes you want, after you’ve added lead to make weight, you’re back where you started.

Conclusion – lowering the rotational mass on a kart might give you some small improvement as far as options for weight distribution/ballast, but it makes no difference whatsoever to the rate of acceleration of the kart, therefore no gain in lap times.
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Scott

[Pete Muller]

[Mike Goebel]

I think you are using a funny coordinate system. The chain accelerates regardless if the kart is on the ground or the rear wheels are off the ground. It accelerates relative to the coordinate system on the kart. The real thing is that the total inertia of the kart is so great in magnitude compared to a single component that reducing a brake rotor mass has negligible performance advantages.

Mike G.

[Brian Naumann]

Couldn't really follow your thought process after 8 hours of work, but look at it this way - a rotating part on a moving kart has two distinguishable but proportional energies, translational and rotational. Translational energy is .5*m*v^2, and rotational energy is .5*I*w^2. I'm sure you recognize the m as mass and the v as velocity, but if you doubt the "marketing" you may not be familiar with I, the mass moment of inertia, and w (supposed to be the Greek letter omega), angular velocity.

In a standalone body these energies can be independent of one another. It can be spinning in one place, it can be moving linearily without spinning or some combination thereof. It takes energy to spin something up, and it also takes energy to move something linearily.

Put your kart on the stand and run it. It takes energy to spin up the rear axle with the kart sitting there. It the wheels, tires, axle, rotor, sprockets, etc. were heavier, they would most likely have a higher mass moment of inertia, and it would take longer to spin the axle up to x rpm. Now if the kart were on the ground, it would take the same amount of energy to spin up the axle assembly, plus, whatever energy it takes to move the kart forward.

You notice in the beginning I said "distinguishable *but* proportional", and then I talked about the energies being independent of each other in a standalone body. Neglecting wheelspin, clutch slip or any similar phenomena, the angular velocity of every component in your drivetrain is directly proportional to the linear velocity of your kart. So if you want to accelerate the kart, not only do you have to apply enough energy to move the total mass of everything linearily, you also have to tack on the energy required to bring all the rotational parts up to the corresponding angular velocity (rpm).

Consider it a tax - you have to pay the bill for everything you want to move to a certain mph (.5*m*v^2), then you have to tack on the .5*I*w^2 extra for everything that is also going to be spinning when you get there.
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Brian Naumann

[Brian Naumann]

I reread the original post and now I see what you were trying to say. The problem with your thinking is both of the particle motions you described relative to the track are translational, and all the cancelling out and whatnot you were talking about is probably true - when it comes down to it, you are accelerating that mass in a straight line, and it is governed by the .5*m*v^2.

What you were missing is the motion of those particles relative to their own axes that move with the kart. The chain is sort of a bad example, but you can look at it either as 114 links in a straight line being accelerated to whatever velocity they move at between the two sprockets, or as if it was wrapped around a 114 tooth sprocket. It takes energy to accelerate it on the kart at a standstill, plus whatever energy it takes to move it with the kart. The brake rotor also takes energy to spin up (which you were missing) as well as move it with the kart (which I think you were talking about).
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Brian Naumann

[Bob Mosso]

[Pete Muller]

Many, many years ago - - I calculated the difference between a solid 1" aluminum axle and a 1" solid steel axle on my Reed Light enduro kart (yea... it was that many years ago ).

At the rate of acceleration of my enduro kart, the aluminum axle was a .007 hp advantage (seven thousandths of one hp).
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[Mike Goebel]

Man I knew there was somteing to be gained. Tomorrow I'm gettin an aluminum axle.


Mike G.

[Rob Linders]

Mike,
Why don't you buy the axle from your helmet painter. Both of them will give you the same level of performance increase.

[Jim White]

If you search this topic has been hashed over before. I personally have attempted to get the lightest rotating mass I can. I went with the Aluminum axle last year, found my lightest set of hubs etc. Did I notice a dramatic difference in times or speeds on my Yamaha sit up road racer? Not really but my thoughts are its one of those small things. Each individual thing may not be worth much, but put together a lot of small things and it adds up to a bigger thing.
Just my opinion

[Scott McFadden]

Yup
thought all of these examples through, even the huge flywheel argument. And yes, for any rotating mass that is stationary (kart on stand) - Newton's Force mass acceleration law applies in its most basic terms.

trouble is (and this was one of my qualifying assumptions) unless the kart is experiencing wheel spin, the rotating masses on the kart will never accelerate independently of the whole kart (or the linier component as expresses above).

Now if the kart engine was mounted axially, like for example a formula 1 engine, lightening of the rotating components of the motor makes a huge difference, especially considering the 19,000rpm. That's why they end up with the tiny clutches. But when was the last time you saw exotic materials being used in wheel brake and tire assemblies. The materials used are more focused on grip and heat dispersion than weight.

The closer your rotating masses are to the plane of the direction of the kart the smaller the benefit in lightening rotating parts. On a kart all the axes of rotation are perpendicular tot eh linear direction (fore and aft).

In the huge flywheel example, and again given the total weight/mass of the kart remains the same, the weight of the kart and driver in Pete’s example would be 0. So in fact your mass around the rim of the flywheel will accelerate at exactly the same rate if the same force is applied Mass = force x acceleration or acceleration = mass/force. The diameter of the flywheel makes no difference because the larger it is the higher the speed of the outer surface for a given rpm.

I don’t think this can be dismissed quite as easily

The only negative effects I can see in having heavier rotating parts are the potential negative effects of gyroscopic forces. But these only apply with a change in direction so are not really relevant to the argument, and given the relatively low max rpm probably insignificant between the heaviest and lightest rotating kart parts.
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Scott

[joseph hollinger]

[Larry Andrews]

Not to diss anybody...JHMO.

While I completely agree with the more scientific explanations given so far, it seems like the largest radius on a kart is something like 6" and most are something like 1.5". As the radius is the basis for the exponential factor, and it's small in karts, the "tax" that Brian correctly describes seems pretty cheap as it goes. Is it significant relative to the driver's skill and level of competition? It's starting to sound a lot like the 13/26 vs 14/28 gearing discussion again. <shrug>

Now put a set of 18" wheels on a kart and see what happens!

[Greg Piet]

[Scott McFadden]

Actually your example supports my argument as much as not

where gravity is present (constant force) and friction is not (in a vacuum) all objects regardless of their mass, will accelerate at exactly the same rate. When it's straight down the rate of acceleration is 32 ft per second squared.

The inclined plane complicates things a little but not much and it is irrelevant unless there is friction present as its effective force merely counters the force of gravity meaning that the log moves in a different direction and accelerates at a different rate. a simple forces and vectors proposition.

As you add friction (back to something closer to reality) it is a moment force that causes rotation, but only 50% of this force can be said to be in opposition to the force of gravity because gravity is acting on the entire mass of the log, so the friction applies a moment force that is oposite to gravity on the 50% of the log below the axis and nearest the plane, but in the same direction as gravity for the 50% of the log above the axis. The total effect is neutral as far as the logs acceleration down the inclined plane.
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Scott