Weight powered car

modest · 05-20-2009

Quote:

Originally Posted by Turtle

So, why do you say 3 wheels better than 4?

Less weight, I should think. Page 8:

Quote:

Keep in mind that 3 wheels work best for any design.

MOUSETRAP POWERED RACER: WELCOME TO THE RAT RACE

By the same reasoning the frame could be triangular as well as using only 3 legs for holding the weight. To fix a point in space requires a minimum of 3 points (e.g. Bucky's Tetrahedron), so the most efficient designs are often triangular. Are you thinking differently?

~modest

Turtle · 05-20-2009

Quote:

Originally Posted by modest

Less weight, I should think. Page 8:By the same reasoning the frame could be triangular as well as using only 3 legs for holding the weight. To fix a point in space requires a minimum of 3 points (e.g. Bucky's Tetrahedron), so the most efficient designs are often triangular. Are you thinking differently?

~modest

Erhm...no; I don't buy it yet. That page makes the claim

Quote:

Keep in mind that 3 wheels work best for any design.

without any substantiation.

Better how? Steering? What better? Where better? Why better? The weight of 3 wheels is only less if you are talking about using one less of 4 identical wheels.

But I was thinking differently yes, in that I was waiting to see if you were going to claim 3 wheels was less friction, because... (as if) I was going to counter that friction is independent of surface area.

freeztar · 05-20-2009

Quote:

Originally Posted by Turtle

I was going to counter that friction is independent of surface area.

How so?

(or were you joking and it went right over my head?)

Turtle · 05-20-2009

Quote:

Originally Posted by freeztar

Quote:

Originally Posted by Troutle

I was going to counter that friction is independent of surface area.

How so?

(or were you joking and it went right over my head?)

Not joking this time.

Just one of those scientifical factoids stuck in my memory banks. Here's a bit on it.

Friction

Quote:

...Leonardo da Vinci made the first experiments on friction using a rectangular block sliding on a dry, flat surface. His main observations are that:

1) the friction force is independent of the area of the surfaces in contact.

2) the friction force is proportional to the applied load.

These were framed as laws by Amontons in 1699 and researched by Coulomb in 1781, who also noted the distinction between static friction (force needed to start motion) and kinetic friction (force needed to maintain friction). ...

freeztar · 05-20-2009

Quote:

Originally Posted by Turtle

Not joking this time.

Just one of those scientifical factoids stuck in my memory banks. Here's a bit on it.

Friction

Thanks for that Turtle. Learn something "new" everyday!

modest · 05-20-2009

Quote:

Originally Posted by Turtle

Erhm...no; I don't buy it yet. That page makes the claim without any substantiation.

Better how? Steering? What better? Where better? Why better? The weight of 3 wheels is only less if you are talking about using one less of 4 identical wheels.

But I was thinking differently yes, in that I was waiting to see if you were going to claim 3 wheels was less friction, because... (as if) I was going to counter that friction is independent of surface area.

Well, yes, from the standpoint of weight only, whatever 4 wheels you choose you will benefit from subtracting one. There's no real need (as far as I can see) to compare 4 wheels of one type to 3 wheels of another type. The point would be that the most-efficient wheels of any type times 4 weighs more than the most efficient wheels of any type times 3.

The friction of a rolling wheel (not the friction of the axle) is called rolling resistance. We should be able to demonstrate that the greater the number of wheels, the greater the rolling resistance. Rolling resistance is:

$F=C_{rr}N_f$

where $C_{rr}$ is the rolling resistance coefficient—a dimensionless number that depends on the properties of the tire and road. It's normally about .001 and we'll give it that number. $N_f$ is the normal force and must be calculated:

$N_f=\left(\frac{m_c}{w}+m_w\right)g$

where,

$m_c$ = mass of the car without wheels (1.5 kg)
w = number of wheels
$m_w$ = mass of wheel (0.1 kg)
g = gravitational acceleration (9.81 m/s^2)

With these made up numbers we can solve the rolling resistance per wheel in the case of both 3 and 4 wheels. The normal force for 3 wheels:

$N_f=\left(\frac{1.5 \ kg}{3}+0.1 \ kg\right)9.81 m/s^2 = 5.886 \ Newtons$

For 4 wheels:

$N_f=\left(\frac{1.5 \ kg}{4}+0.1 \ kg\right)9.81 m/s^2 = 4.660 \ Newtons$

Having the normal force we can calculate the rolling resistance for each wheel. For 3 wheels:

$F=C_{rr}N_f=0.001 \times 5.886 \ N = .0059 \ N$

and for 4 wheels:

$F=C_{rr}N_f=0.001 \times 4.660 \ N = .0047 \ N$

So, each wheel on a 3-wheeled car has more rolling friction than each wheel on a 4-wheeled car. But, we need to find the total friction which means multiplying by the number of wheels in which case we find there is more total rolling resistance for a 4-wheeled vehicle than an equivalent 3-wheeled vehicle:

Total rolling resistance for 3 wheels:

$F_{total}=F \times w = 0.0059 \ N \times 3 = 0.0177 \ N$

Total rolling resistance for 4 wheels:

$F_{total}=F \times w = 0.0047 \ N \times 4 = 0.0186 \ N$

All else being equal then, it's best to go with 3 wheels as opposed to 4 equivalent wheels (if I've calculated the above correctly

)

~modest

Turtle · 05-20-2009

Quote:

Originally Posted by modest

Well, yes, from the standpoint of weight only, whatever 4 wheels you choose you will benefit from subtracting one.

This presumes of course no weight change in the frame of 3-wheel vs 4-wheel, as it is the total weight which affects the outcome. Nevertheless, I give you a push.

Quote:

Originally Posted by Mr. Modest

The friction of a rolling wheel (not the friction of the axle) is called rolling resistance. We should be able to demonstrate that the greater the number of wheels, the greater the rolling resistance. Rolling resistance is:

$F=C_{rr}N_f$

where $C_{rr}$ is the rolling resistance coefficient—a dimensionless number that depends on the properties of the tire and road. It's normally about .001 ...

But the axle is rolling friction/resistance too, correct? You're just not calculating it? And then, just a check on how you arrived at that "normally .001" coefficient as you said "tire" and I read a lot about rubber tires being a different ball of wax when it comes to calculating rolling resistance.

From what I recall, a "tire" and surface of non-deforming material has a rolling resistance coefficient virtually equal to the coefficient of the sliding friction of the two materials. (it's late but I'll try & find a link tomorrow.

)

Quote:

Originally Posted by modestimator

Total rolling resistance for 3 wheels:

$F_{total}=F \times w = 0.0059 \ N \times 3 = 0.0177 \ N$

Total rolling resistance for 4 wheels:

$F_{total}=F \times w = 0.0047 \ N \times 4 = 0.0186 \ N$

All else being equal then, it's best to go with 3 wheels as opposed to 4 equivalent wheels (if I've calculated the above correctly

)

~modest

I only see the one calculation error.

It's in your favor though.

0.0047 * 4 = 0.0188

modest · 05-21-2009

Quote:

Originally Posted by Turtle

But the axle is rolling friction/resistance too, correct?

If you're using ball bearings then I suppose it is. But, with a simple axle/bearing like depicted here:

-source

the friction is not rolling, but kinetic—much like one plane surface sliding on another. Or, more accurately, like a rod sliding on a plane surface (but not rolling over the plane surface).

Quote:

Originally Posted by Turtle

You're just not calculating it?

Indeed. The friction from the axle should be independent of the number of wheels. The extra weight from extra wheels would not be carried by the axle, so the normal force for the axle would be the same regardless.

Quote:

Originally Posted by Turtle

And then, just a check on how you arrived at that "normally .001" coefficient as you said "tire" and I read a lot about rubber tires being a different ball of wax when it comes to calculating rolling resistance.

I guess I should have used the word "wheel". The coefficient 0.001 is typical of materials that do not deform much like a train wheel / rail. If the wheel were rubber or the ground were soft like sand the coefficient would be larger. For a car tire on asphalt it's ~0.015.

The coefficient (like other friction coefficients) is empirical meaning it must be measured rather than calculated.

Quote:

Originally Posted by Turtle

From what I recall, a "tire" and surface of non-deforming material has a rolling resistance coefficient virtually equal to the coefficient of the sliding friction of the two materials. (it's late but I'll try & find a link tomorrow.

)

I don't think that could be right. The friction of a rolling wheel would be quite a bit less than a skidding wheel. It's easier, in other words, to roll a wheel than to drag it along.

I think what you may have read is that a spinning axle in a bearing has a coefficient of friction nearly equal to the sliding friction coefficient of the two materials. That's true:

Quote:

Axle Friction—It has already been pointed out that the coefficient of axle friction is not necessarily the same as that for the plane surfaces sliding on one another, and, besides, the continuous contact of a shaft and its bearing is very different from the brief contact occurring in sledge experiments. Morin however made special experiments on the friction of axles and showed that the coefficients were constant and nearly the same in the two cases.

Applied mechanics: an elementary ... - Google Book Search

Quote:

Originally Posted by Turtle

I only see the one calculation error.

It's in your favor though.

0.0047 * 4 = 0.0188

Oh, sorry. I rounded 0.0047 when I copied it into the post. It had been 0.00466 in excel. My bad.

~modest

arkain101 · 05-21-2009

C'mon, guys we all know if there is 3 wheels, there is much chance than with 4 to drive over the granola bar and cookie crumbs spread out along the race track from the cheering fans, not mention the grains of sand tracked from the outdoor footwear.

Sweep the track good and even before a race!

arkain101 · 05-21-2009

In my experience with racing of vehicles and motorcycles it is a well known fact that a longer vehicle has greater strait-line stability, which translates into faster top speeds, greater acceleration, and more efficient use of energy.

The rake angle is one of these important factors.

That is, if you arrange your steering axis so that it perpendicular to the road service, any unwanted slack is going to be magnified in how it affects the strait line stability.

So a lot of fine tuning is done so that the rake of the steering axis is set back into the negative angles(imagine a harley chopper with the long front forks). This way, any uncontrollable wobble or misdirection is reduced and stability is maintained, however it comes with the trade off of losing tight turn ability and traction.

As such it is more intelligent to have a steering axis (swivel point) that is extended by a distance (radius) from the actual axle or arranged so that it is leaned back when precise steering and greater room for error is desired.

Weight powered car

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