Weight Placement

General topics of interest to racers and race coordinators alike.
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Stan Pope
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Re: Weight Placement

Post by Stan Pope »

SlartyBartFast wrote:Here we go again, I come back from a long hiatus and get sucked in to thinking these things through and I start jumping in on threads (probably half-cocked).
We need someone who can inject some real knowledge into the discussion! We're counting on you!
SlartyBartFast wrote:
Stan Pope wrote:In this case, measure the moment of inertia as the car "spins" about its CM.
My muddled memory and the time since my last physics and dynamics class aside, the car most certainly does not spin around its CM.

As the car goes around the transition curve, there are two points around which it rotates. The rear axle as the nose lifts, and the centre of rotation which is probably somewhere off above the car. The center of rotation is dynamic and depends on the wheelbase and the track curve.

Given those two centres, although that's probably muddled as one is related to the other, the distance between the centres and the CM give you the inertias and momentums.
I have followed usual practice of analysis ... first analyze the energies as the components of the car rotate about the car's (moving) CM, then, second, analyze the energies as the car's CM rotates about the track's center of curvature. If you choose a point on the car other than its CM, then the second part of the process gets a lot more complex.

Set me straight! Please!
Stan
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SlartyBartFast
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Re: Weight Placement

Post by SlartyBartFast »

Stan Pope wrote:I have followed usual practice of analysis ... first analyze the energies as the components of the car rotate about the car's (moving) CM, then, second, analyze the energies as the car's CM rotates about the track's center of curvature. If you choose a point on the car other than its CM, then the second part of the process gets a lot more complex.

Set me straight! Please!
I'm not sure I can set you straight. I'm much more adept at asking questions than providing answers. :p

I have a big problem with the first considering the car's CM (centre of mass right?) as a fixed point with the components moving around it. The CM moves around some point. It is the moving CM that gives you inertia, energy, and momentum.

I've no problem with the second (CM curving with track).

So, for the first, the center of rotation for pitch is the rear axle. The nose goes up as the car transitions from drop to horizontal. The center of rotation for yaw depends on how much the wheels are slipping and where the car was hit to induce a turn.

Now, intuitively, this would make me think:
- Maximise inertia for Yaw.
- Minimize inertia for pitch but control maintaining front wheels sufficiently weighted on track while transitioning from curve to horizontal.
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FatSebastian
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Re: Weight Placement

Post by FatSebastian »

Stan Pope wrote:If you choose a point on the car other than its CM, then the second part of the process gets a lot more complex.
Application of the parallel-axis theorem simplifies the analysis.
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Re: Weight Placement

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SlartyBartFast wrote:I have a big problem with the first considering the car's CM (centre of mass right?) as a fixed point with the components moving around it. The CM moves around some point. It is the moving CM that gives you inertia, energy, and momentum.

I've no problem with the second (CM curving with track).
Think in terms of "frames of reference".

The frame of reference for the first part is simply rotating, no "translation".
For the second part, the rotating frame of reference is arcing around the track's center of curvature, i.e. only translation!

As I think about this more, the path of the CM, once both front and rear wheels are on the curve, is circular. But, during the transitions into and out of the curve, when one set of wheels in rolling straight and one set is curving, the path is not so simple! The rear axle path, on the other hand, is simple .... straight line, circle, straight line! So it is probably the simplest path for analysis!

Good catch, SBF!
Stan
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Re: Weight Placement

Post by Shawn Stebleton »

SlartyBartFast wrote:- Minimize inertia for pitch but control maintaining front wheels sufficiently weighted on track while transitioning from curve to horizontal.
This is exactly what my sons and I tried to accomplish with the vertically-oriented tungsten plates in the location they were placed. I couldn't have said it better!
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Re: Weight Placement

Post by Speedster »

Shawn, does the wing extend the stock distance from axle slot to end of block? Do you race on a Best track? How much clearance do you have when the car goes through the curve?
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Re: Weight Placement

Post by Shawn Stebleton »

We have to use slots, but cut off the back and add to the front. The pack races on a Piantedosi Classic wood track and lately the district has used an old Best Track with the sharp 2' curve.

I haven't measured clearance, but it has never been a problem. We've run on the tight curve Best Track only the last three years, and have tapered the underside up a small amount each of those three years, thinking that we need to make sure it clears, but after seeing all the cars that run on that track I think that it isn't a problem. Most of them have the back axle slot as far back as possible, and many have an underside that hasn't been tapered up, and they run just fine on that 2' radius curve.

We use the Pro Body Tool to ensure the nails go into the right spot in the axle slots. We have more than 3/8" clearance underneath the front of the car. The weights do hang down a bit, but they're right by the rear axle and don't cause a problem. In fact, this year, his car had only 5/16" under the weights.

If you give the DFW a negative camber (axle head angled down), it will lift the front of the car just a bit, anyways.
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Re: Weight Placement

Post by Speedster »

Thanks for all the info.
I know it's just a typo but the axle head pointed down would be Positive camber.
Thanks again.
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Re: Weight Placement

Post by Shawn Stebleton »

Yes, positive camber. My bad. I had a thought in my head for a different topic about running the back axles flat vs negative camber when I wrote that above. Thanks! At least it's hard to get the axle head pointed down mixed up!
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Re: Weight Placement

Post by FatSebastian »

FatSebastian wrote:Application of the parallel-axis theorem simplifies the analysis.
:idea: I think this theorem may explain mathematically why we have never wrung our hands over concentrating mass at all costs v. using tiny trim weights as necessary.

The theorem states that the mass moment of inertia (MoI) about the pitching axis equals the MoI about the CoM plus the mass m times d squared, where d is the horizontal distance between the pitching axis and CoM axis:

Ipitch = ICoM + m x d^2

It is the rotation about the pitching axis halfway between the axles that seemingly counts when determining the energy loss during transition, and the contribution of the m x d^2 term ends up being several times larger than the MoI about the CoM.

As a numerical example, Jobe's book on p. 110 provides the estimated mass MoI of his so-called "JNTS car" (p. 401), which DT'ers would recognize as a "rail car" design per Stan Pope. Jobe's version is ¼" thick, has an extended wheelbase, has a solid Pb tail end (the rear axles fit in the lead, not wood), and maintains only 12 grams (0.4 oz) on the DFW (p. 219). The CoM is reportedly located about ½" in front of the rear axles, or about 5.7" from the front of the seven-inch-long car. Jobe measured the mass MoI about the CoM at 1909 g cm^2. However, the m x d^2 term will contribute more than 4000 g cm^2 additionally to the pitching MoI on the track—more than tripling the effective mass MOI—despite the efficiency of this design.

Thus, if the pitching MoI really is an important design criterion in a PWD car, then perhaps more attention ought to be paid to minimizing d by moving the pitching axis closer to the CoM? This would be accomplished by moving the front wheel(s) backwards—as close as possible to the CoM. (The alternative would be to move the CoM forward. :( ) Meanwhile, a one-gram trim weight near the front wheel would probably add ~170 g cm^2 to the mass MOI, or ~2% to the total pitching MoI, which could also be compensated for by moving the front wheel back just a tad.
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Re: Weight Placement

Post by Speedster »

No doubt this is all true. If I recall correctly this was discussed between Stan Pope and Sporty. I think it ended up with Sporty stating that extended wheelbase cars were easier to tune. The Mid America races seem to confirm that. Maybe it's far more complicated than that. If one small section of the track (Best track curve) is concentrated on and a "Perfect" car is designed for that small portion then it will be the best for that small portion. However, on both sides of that curve there's a lot of track and it may take an entirely different designed car to do well on that large portion. If we really knew what happens on the entire track perhaps a car could be designed to take advantage of all portions.
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Re: Weight Placement

Post by SlartyBartFast »

FatSebastian wrote:pitching axis and CoM axis:
I don't mind admitting that there is far more theory and math in the link than I care to try to wrap my head around.

But my mind screams out when I read "CoM axis". Just the simple physical reality of the car/track interface, in my mind, shows the impossibility/impracticality of using rotation about centre of mass as any valid measuring point of car performance.

Moving the CoM doesn't alter the reality of the track/wheels, and doesn't change how the car rotates. Vertically, the two pairs of axles are held parallel to the track surface (unless the front raises due to inertia leaving the curve).

Starting the discussion by considering a "CoM axis", just doesn't convince me the rest is going to follow.

The CoM most assuredly affects how the car behaves in the transition from curve to flat (do the wheels raise up) and how the car might behave to forces applied parallel to the track surfaces.

Maybe it's a frame of reference thing. Can anyone explain the reasoning to me? There are obviously a number of accepted terms and references I am not following.
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Re: Weight Placement

Post by FatSebastian »

SlartyBartFast wrote:Just the simple physical reality of the car/track interface, in my mind, shows the impossibility/impracticality of using rotation about centre of mass
Correct. The energy to rotate ("pitch") a car will be proportional to its mass moment of inertia as measured about the axis of rotation (not the CoM axis) and the square of rotation rate about the axis of rotation (not the CoM axis). (I called the axis of rotation the pitching axis.) Rotation about the CoM is not involved.

Mass moment of inertia measures the extent to which an object resists rotational acceleration about an axis, and its value will change depending on the location of the axis of rotation—even for the same object. However, it is usually easiest to measure and describe physical properties relative to the CoM versus any other arbitrary axis. So the theorem merely says that if one has already measured the MoI about the CoM, and one also knows the location of the pitching axis relative to the CoM, then one can easily compute the MoI about the pitching axis of rotation. Again, rotation about the CoM is not involved. The point of reference is the pitching axis about which an object seems to rotate (which in this case would be in a plane about halfway between the front and rear axles).

My point was that the parallel-axis theorem seems to show the total pitching MoI being several times larger than the more familiar CoM MoI. So tweaking the MoI with respect to the CoM is actually a small contributor to total pitching MoI. The pitching MoI is significantly affected by d^2, which is a function of the wheelbase.
SlartyBartFast wrote:Starting the discussion by considering a "CoM axis", just doesn't convince me the rest is going to follow.
Actually I started with "mass moment of inertia (MoI) about the pitching axis." My apologies if the discussion was less than convincing (or erroneous); fortunately, the correct physics happen regardless of whether we are convinced that they will.
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Re: Weight Placement

Post by FatSebastian »

Speedster wrote:Maybe it's far more complicated than that. [...] If we really knew what happens on the entire track perhaps a car could be designed to take advantage of all portions.
Yes, although one must remain cognizant of the relative benefits. How significant is the energy lost from rotational transition relative to other performance aspects? Assuming a sharp transition, theoretical calculations by Jobe suggested that this effect is on the order of a millisecond in terms of total race time—which is approaching the resolution of many timers. Yet there may be other performance benefits arising from concentrating the mass that are unrelated to rotational transition. If we optimized the transition pitching moment to theoretically gain a fraction of a millisecond (by introducing an extremely short wheelbase, for example), this would almost certainly be at the expense of performance elsewhere.

IMO, the Go-ask-Grandpa flex car is a great example of theorizing to optimize a singular performance parameter—to the detriment of total performance. The design hinges on the assumption that "noise is lost energy" and "a car that rolls easily and quietly on a rough surface is going to win the race." Although the design is imaginative, in practice flex cars are reputedly hard to tune and simply not as competitive as more conventional designs.
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Re: Weight Placement

Post by Speedster »

I agree.
Love the Flex cars. I've never seen anything like that before.
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