# More friction questions

We did a few rover wheel robot tests today and based on what I saw I am puzzled. It appeared that a lighter robot would accelerate faster then a heavy robot. Lets see if I can throw out some formulas
**
Heavier**
533.8 N (120 lbs) (54.47 kg on earth) robot
Ff= µ • Fn
x = .05 • 533.8
x= 26.69 N
a=F/m
.4899 m/s^2 = 26.69 N / 54.47 kg

Lighter
400.3 N (90 lbs) (40.82 kg on earth) robot
Ff= µ • Fn
x = .05 • 400.3
x= 20.02 N
a=F/m
.4904 m/s^2 = 20.02 N / 40.82 kg

In standard units, the lighter robot will accelerate 0.0164 ft/s^2 faster.

Based on these numbers, unless I did something wrong, a lighter robot would accelerate faster on regolith then a heavier one (admittedly a small difference). So teams that are talking about adding weights to their robot to add friction should reconsider.

40.82 * 9.8 = 400.03

to 4 digits this rounds to 400.0 not 400.3

Don’t forget the trailer! More robot weight would reduce the relative effect of the trailer, yes?

I actually got this number by converting 90 lbs directly into Newtons, as they both measure force.

Yeah, I feel like this is more important.

another thing to consider is that if your robot skids out due to less fricitonal force because of the reduced weight (Force friction = mg x coefficient of friction) you have to use the coefficient of kinetic friction in the equasion which is less than the coefficient of static friction used when the robot is rolling.

It makes perfect sense to me. Think of 2 cars with equal power rolling at ten miles an hour. One car is 500lbs heavier than the other. The lighter car will accelerate faster with the same power because it takes less energy to accelerate.

When you actually observed this difference in acceleration were both robots moving or were they stationary? Traction doesn’t have as great of an effect once your moving beyond a certain speed. If they were stationary the heavier robot should accelerate faster to a point because it’s wheels are spinning less but the lighter robot should overtake it once it gets traction. (think drag racing)

This is a point I keep bring up with my team. I think it’s better to design to be lighter and then be able to add weight for traction than to design heavier and be stuck with it.

Right but I’m proposing is the momentum of a light bot will be easily controlled by the friction of the wheels, even if that friction is less. So a heavy bot will be less willing to slow down based on the friction then a heavy bot. The change in friction shouldn’t change anything because both robots encounter the same change.

Yes. The mass of the robot and trailer need to be accelerated, but only the weight of the robot and a little bit of the trailer adds to the tractive force from the driving wheels.

Well a lighter robot will have less frictional force but also have less inertia… so I think the effect cancels out. As far as the car analogy, we are limited by friction, not power (did you see 2 vs 4 motor test on kickoff?). Therefore teams should shoot for 120 lbs since it reduces the relative effect of the trailer and other robots. Along with that the cg should be towards the rear wheels to help turn with the trailer.

As Mark Leon would put it “This is why we do the math”. You brain can convince you anything makes sense, do the math to find out.

I’m sorry… did you mean you experimentally tested and the lighter robot accelerated faster? The difference in the equations is due to conversion/rounding errors (try it with just 50 kg and 40 kg), but perhaps there’s a factor we’re not accounting for. For example, it takes less power to spin the wheels on a lighter robot.

I was saying that basing ideas off what you believe will happen rarely works in my experience, especially concerning physics. I did no scientific method testing, but noticed some odd responses from playing with the robot and did the math behind it. And I would love for someone else to try the same thing, after all nothing is sure until its repeatable.

PS Once you move into dynamic friction (slipping wheels) it does not matter how fast your wheels are spinning you get the same force response.

You’re right, I probably shouldn’t jump to conclusions so quickly. On Monday I’ll experiment with different weights on our test chassis. We’re also assuming the wheels and this surface follow the formulas perfectly.

As far as dynamic friction, I know you get the same force, but I was suggesting control implications since it would take less movement of the joystick to make the wheels spin.

Work with just the variables and see that weight makes no difference in acceleration:

Ff=uFn
Fn=9.8m

Ff=9.8um

Fnet=ma
Ignoring air resistance, Ff=Fnet
Ff=ma=9.8um
9.8u=a
u=.05
a~.5 m/s/s, no matter the mass of the bot.

Well that explains why the numbers were so close. (~.0005 m/s^2 difference)
Thanks!