Creating a timing correction factor for weight differences in karting

[gills]

Hey all, this is long so read if you like anything to do with motorsports and let me know what you think.

My friends and I (currently in junior year as ME student) are going to a high performance karting facility for some good racing and I wanted to do something as a fun little project. Unfortunately, we are not in a league where they actually add ballast to the karts to even out the weight differentials between all drivers. So, I've decided to attempt to come up with a alternate solution analytically where I can add on a specific timing correction based on the weight of the driver, using the heaviest guy as the reference. I'm doing this because the weight-to-power ratio of these karts is much greater than a high-horsepower sports car where a difference in 30lbs between two people won't make a difference really, but on a 6.5hp kart it is substantial.

Now before I start, obviously not all karts are created equal, and there are other factors that will affect lap times that are beyond analysis. But, I'm assuming that all these karts are equal (alignment, tire wear and grip, chassis dynamics, power delivery, etc..) for the purpose of this little project. All of us all have track experience (karting and car) and these karts are about as equal as we are ever going to get short of a spec racing series. The only real factor I want to differentiate our lap times is our driving technique and skill.

Some info: the karts all have a 6.5hp honda engine equipped with a continuously variable transmission (CVT) that have a top speed of 40mph. They are all the same make chassis and have the same tires. The track contains 6ft of elevation change in one location and a straight long enough to hit 40mph from a standstill at the start of the race.

Obviously weight is a major factor whenever there is any type of acceleration involved so i figured the easiest place to start would be during the 0-40mph drag race at the start of the race. During this, I'm saying that power output is constant at 6.5hp from the instant we all hit the gas to the time we reach 40mph, which i think is reasonable since this is essentially what CVT's do (although I don't think it is quite peak power, but close). Using the relationship that P=F*v, F=ma, and a=dv/dt, I made an excel spread sheet for velocity from 0-40mph at high resolution and found the corresponding force at each velocity at a constant 6.5hp. From there i found the acceleration at each point. Then for time it was the difference in velocities at adjacent points divided by the average acceleration between those two points, and then summed. This is what I obtained using the heaviest guy as the reference:

mass [kg] Correction Factor str8 line acceleration [seconds]
179.138322 0.149987914
183.6734694 0
172.3356009 0.374969785
172.3356009 0.374969785
170.0680272 0.449963742
167.8004535 0.524957699

Next I calculated how much time it takes to do the work of lifting our weights 6ft in elevation with 6.5hp during each lap: time = mgh/Power (disregarding friction, which I'm sure is ultimately benefiting the lighter guy).

So during a 20 lap race, with one all out drag race, I get this (corresponding to the same weights as above):

Total Correction for 20 lap race [seconds]
0.484811378
0
1.212028444
1.212028444
1.454434133
1.696839822

Just wondering if this is reasonable or not and what you think can be easily included into this. I really want to try and include the effects of turning with extra weight into this with everything being equal except for weight (turning radius, entry velocity, tire grip, etc.). Obviously extra weight is a big factor in cornering capability because the tires need to do more work to keep from sliding. The heavier guy will almost always get the tires to start sliding before the lighter guy if they enter the turn at the same velocity and turning radius due to the extra momentum he is carrying. In 6.5hp karting this is a big no-no because speed will be scrubbed off big time and to accelerate back to speed for the big guy compared to the little guy is substantial. I wanted to try and incorporate this kind of difference into this, but it seems to be very complex.

An argument my lightweight friend (not in engineering) keeps making is that because of extra weight, the heavier guy has more friction from the tires because the frictional force is proportional to the weight of the object allowing us to turn-in better. He claims that sometimes when he goes karting he can't get the front tires to bite on turn-in and they slide where the heavier guy would have the extra friction needed. Sort of like aerodynamic downforce. In every free body diagram I've drawn of a body undergoing centripetal acceleration with a frictional force, mass gets canceled out in the equations. It's been a while since dynamics so, is this correct?

Now i understand that the system of a tire is very complex (conforms and deforms to the road surface, differing physical properties as a function of temperature, etc.) and that mass plays an integral role in the traction of the tire, and with more mass --> wider tire is required. The tire at the microscopic level does more work with more weight on it, which generates more heat and increasing the surface area of the contact patch allows for the heat to be dissipated more effectively. But, is what my friend saying reasonable at all and how could I possibly incorporate turning into my analysis?

Sorry for the huge post and if you reply, I'd greatly appreciate it.

 

[Ranger Mike]

Drag racers say 100 lbs reduced is ~ .1 or 1/10 sec again ~ 10 hp gain/ 100 lbs reduced.
so ifin yo ucan shave off 100 lbs. performance improves at same as adding 10 HP
30 lbs off is like adding 3 HP
weight to Hp ration goes up big time
thing to remember when up against to strict rules is
look at what you can do to make more HP
and reduce weight
like any elimonation of rotating weight is huge
for every 1 pound rotating weight you take off, the kart thinks it lost 10 pounds static weight
a few things to think of
are you running tubes in the tires? go tubeless save weight
sprockets all drilled to lighten um?
gun drilled axles?
brake calipers drilled to lighten?
flywheel shaved?
can you shave the crankshaft
lighten con rod/piston wrist pin weight?
light and low makes it mucho better

 

[mgb_phys]

Modelling the turning and braking of the carts is going to be tricky - I would try some experiments, same driver, same cart and add some lead weights.

Consider cornering.
You can accelerate faster with less mass - that's pretty simple
You also need less braking force (or can brake faster) with less mass.
More mass gives you more force on the wheels and more grip (the wings on an F1 car double the effective weight)
But more mass also means you need more sideways force in a curve to stop you simply flying off the side.
Then there are more complex considerations - if most of the mass is the driver, how much can they move? Can a driver lean sufficently to affect the force on each wheel - as an active control system?

edit. Straight line drag racing is much simpler - all you are interested in is, f=ma

 

[gills]

Modelling the turning and braking of the carts is going to be tricky - I would try some experiments, same driver, same cart and add some lead weights.

Consider cornering.
You can accelerate faster with less mass - that's pretty simple
You also need less braking force (or can brake faster) with less mass.
More mass gives you more force on the wheels and more grip (the wings on an F1 car double the effective weight)
But more mass also means you need more sideways force in a curve to stop you simply flying off the side.
Then there are more complex considerations - if most of the mass is the driver, how much can they move? Can a driver lean sufficently to affect the force on each wheel - as an active control system?

edit. Straight line drag racing is much simpler - all you are interested in is, f=ma

Unfortunately i can't do experiments. If i could, i wouldn't be doing this:)

I have straight line compensation already as i mentioned in my original post and the time difference of lifting our weights 6ft with 6.5hp. It's obviously not quite 6.5hp due to driveline inefficiencies, so I may adjust that.

As far as cornering, there will be a good deal of assumptions obviously. Equal COG, equal tire grip, equal everything except for weight is what i want to do. No one is squirming around so there is only weight transfer from the COG of the system that is assumed to be at the same location for everyone.

I think I need to find an actual lateral force vs vertical load plot for the tires and manipulate that to get the data i need. The coefficient of friction for tires decreases as you load them more so I just need to find out this relationship for the tires used on the kart, which is probably impossible.

Anyone else have any ideas?

 

[gills]

Ok, I've come to the realization that analyzing cornering is ridiculously difficult. In order for me to do it accurately at all, i need actual test data of the tires themselves.