Go-Kart Physics: Math for Senior Project Due in a Week

[t_olhanoski]

I am a senior in high school and am working on a project with one other partner for our engineering science class. We decided to build a go-kart for our project, which we have nearly completed. It is not powered by a conventional gas motor, but instead by a car alternator (essentially just a DC generator) that is powered by two car batteries. We need to write a term paper and give a presentation on our project. the only thing we can't figure out, is what math do we use? I know we can measure velocity and acceleration and the power output, but I was wondering if anyone else had some ideas for potential math computations that can be performed. Anything would help. Thanks.

(by the way, the project is due in a week)

 

[duodoublescythe]

Im an engineering student at Western Carolina University and right now I'm dealing with about the same problem, we're designing model car and we have to determining the speed, acceleration, power needed to induce movement, rate of decelreation, the amount of force needed to power the motor and a bunch of other things like gear ratios and coeficient of friction. Just throwing some ideas out at you. Sorry couldn't be any more help.

 

[enigma]

You can do some analyses to find out the fastest turns it can handle without tipping over. You can do some analyses to find out how big a driver the go-cart can support. You can come up with range off of a battery.

 

[Danger]

To extrapolate upon Enigma's post, you should definitely look into the various spring qualities in your suspension system, which will determine both of the factors that he mentioned. 'Go-carts' as a generic term covers an awful lot of territory. I remember one that I saw at the sports shop when I was buying my .44; it had two 750 Kawasaki engines (one driving each rear wheel). Top speed on that sucker was over 100 mph. I also remember Fred Goeski's 'go-cart' that he used as a demonstration rig at the drag strips. It had the same little bitty go-cart wheels and platform, with a 10,000 hp peroxide rocket on the back.

 

[t_olhanoski]

To clarify, this cart was made in a matter of two to three weeks. It is the most basic it can possibly be, as we are limited on both time and monetary resources. Our suspension system is actually nonexistent. Because of the fact that it is an electric powered cart, its speeds will not be that significant. Anything that involves very complex mechanics cannot be found on our cart, which is why we aer having trouble with different things to measure.

 

[Danger]

You could demonstrate the rationale behind ion engines by altering your gear ratios. Steep gearing can get you to maybe 10 mph in a hurry, but no faster (chemical rocket); shallow gearing will take you a lot longer to reach 10 mph, but you'll keep slowly accelerating to 20 or so (ion drive). Those numbers are just out of the air; I have no idea what the actual ones would be. The math involved would pretty much just be straight-forward acceleration figures.
You could also try to calculate the friction numbers for various types of bearings if you have the option of swapping them. Compare your acceleration and top speed using bushings, ball bearings, roller bearings, etc..
Although I don't know much about electricity, I would expect that there are also measurements that you can take of the power system, such as resistance changes or whatnot in the motor under various loads.

 

[enigma]

Well, the top turning speed can be calculated just from the center of mass and the wheelbase. You don't need to be able to attain the speed... just find what it is.

 

[Danger]

But that takes away the fun of watching your best friend go ass-over-teakettle into a tree.

 

[Cliff_J]

Few thoughts that may/not help:

An alternator wouldn't work and the term shouldn't be used. An alternator is a AC generating device that rectifies the output to end up with DC.

If it runs on DC, it could be a series wound motor (like used in a hand drill and can run on AC or DC) or a permanent magnet DC motor. A PMDC can also be used as a generator.

Every motor will have a series of graphs for current/RPM/power. At zero RPM (stall) the motor will generally use the most current and create the most torque. Beware its a hazardous condition because large currents can cook the battery, motor, and wiring and smoke things! Anyways, at 1/2 max RPM the power will generally peak, and at max RPM the torque will be effectively zero. Only rough rules of thumb that vary based on motor construction, but should be somewhat correct.

So based on the motor graph and load (weight/drag/gearing) presented to the motor, the acceleration will actually vary through time on a curve. You could vary the load by the weight of cart + cargo and gearing to show its effects and how optimizing weight (assuming no-budget aluminum or carbon fiber) or even things like low rolling resistance tires etc affect the overal numbers. Also lots of possibilities exist around battery life calculations that hinge on using the motor at its maximum efficiency (somewhere in the middle to high of its RPM range usually between max power and max RPM) and loading it properly.

Batteries have a capacity in Amp-hours but as you draw more current the time goes down on a curve again, so speed/range etc are all dependent on each other. Add to the above and now there are many factors to predict range/speed.

Steering geometry on carts (even RC cars and definitely regular cars) will most times have ackerman built into them to steer the left and right tires at different angle to compensate for the different sized circles when turning. Google and you can find equations involving the appropriate angle based on the turn radius and allowing the tires to remain tangent to the respective circles.

If that's not enough math, the temperature of the battery, electric motor and so on are important as would the gauge of wire and associated voltage drop from the flowing current etc could be factored in. If you dig deep enough, there's always a little more math behind the scenes of even the simplest setups...

 

[Danger]

Great post, Cliff. Thanks for pointing that stuff out.

 

[Cyrus]

Oh, that reminds me cliff, there is steering caster and camber as well. Its what causes your steering wheel to self center if you turn it hard over to one side and press on the gas while keeping your hands off the wheel. The other keeps the car tracking in a straight line.

 

[Cliff_J]

You're welcome, I found a link with a couple more things to hopefully clear up any ramblings I made earlier:

Good website about building electric cars - not super easy but with a little persistence you should find lots of info:
http://www.greenpower.co.uk/design.htm

A motor performance graph - kinda difficult to read (motor is stalled at the right of the graph) but once you look at it a little bit you should be able to derive your own rough rules of thumb assumptions to work from:
http://www.greenpower.co.uk/Greenpower%20Motor%20Datasheet.pdf

Some nice battery discharge math, far more applicable if you're using lead-acid car batteries than if you used hundreds of NiCad/NiMH/LiOn batteries but still interesting to see how applicable the Ah rating really is at higher discharge levels.
http://www.smartgauge.co.uk/peukert2.html

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Actually cyrusabdollahi, you're thinking of the term toe-in where the wheels are actually slightly steering towards each other as a means of keeping a vehicle running straight down the road and avoiding the 'sneeze-reflex' steering that most people would call twitchy. And yes caster can provide the ability to cause the wheels to straighten out automatically, caster is used in the front wheels of shopping carts to allow them to automatically track.

Camber is the vertical tire angle to the surface, and its used more in performance applications to keep the tire tread as parallel to the ground as possible. Caster will actually affect camber, it makes the tires lean into a turn a little bit so the tire is somewhat flat while the sidewalls roll over a little - the idea is to have the two cancel each other out a little bit. Something like a Corvette will be designed to use this to increase cornering, on a small car designed for younger drivers the camber will sometimes be purposely set to decrease the tire tread contact patch to prevent high speed cornering and keep the car 'understeering' so the driver doesn't get into trouble with an oversteer related spinout where the back wheels would slip out. There's more to it, but isn' there always. And one of Herb Adam's books is on google's book search now, tons more info there.

 

[Danger]

Believe it or not, I was going to mention front-end geometry (I was a bit of a street racer back in the day) until he said that he was working with bare-bones equipment. That led me to assume that he was running straight stub-axle-on-pivots steering. Camber, castor and toe-in are all vital to any reasonably powerful vehicle, but if this thing can't get over 10 mph or so, they aren't necessary. Still, it's good that they were acknowledged.

 

[Cyrus]

I found my auto book "How your car works"-Sam Julty, this is what I should have said to be clear, and I just think are interesting for what their worth:


"There are two regions on the tire where distribution of weight affects tire balance. Those are around the circumference and on both sides of the center line. If the weight is not distributed correctly around the circumference, there will always be a heavy spot. If the wheel is raised from the ground and allowed to rotate freely, the heavy spot will always come to rest on the bottom. In actual operation of the car this imbalance will produce was is called wheel tramp. That is, every time the heavy spot comes around to contact the raod, it actually slams to the pavement. Though the amount of imbalance may amount to only an ounce or two, the "tramping" force of a fast-rotating wheel may be several hundred pounds. This wheel is said to lack static blance. It gets its name from the fact that the test of the wheel balance is done when the wheel is at rest, static. The other kind of tire balance describes the weight distribution between the inner face of the tire and wheel and the otehr face. IF the tire is in balance, the center line of the weight mass coincides with the center line of the wheel.
If one tire face is heavier than the other, centrifugal force will try to transfer the weight to the opposite face every half turn of the wheel. The result is that the wheel will wobble or shimmy. Again, the amount of imbalance will be exaggerated with the motion of the wheel. This wheel is said to lack dynamic balance. The name indicates the condition can only be revealed by a moving or dynamic wheel. Both static and dynamic imbalance are corrected by placing lead weights on the rim of the wheel. The weights are installed opposite the heavy sides"...it goes on to say...
"Camber The word usually refers to a bend or curve. Regarding wheel alignment, camber refers to the inward or outward tilt of each wheel when measured at the top. Camber can be either a "bow-legged" or "Knock-kneed" position."... "camber is the angle of tilt the wheel has toward or away from the frame, as measured from the top of the wheel."

"toe in- is the angle of the front wheels tilted towards the car frame when the car is at rest. In motion, the wheels tend to run in a straight ahead position."

"Caster- is the angle at which the steering knuckle is forward or back."

"Caster. This describes the number of degrees that the ball joins are titled forward or backward from their vertical position when viewed from the side.

I can post more later but I have finals this week and I really should be studying...hehehe oops.

 

[Cliff_J]

Danger - fully understood, this may be a case where the front axle is off a riding lawn mower or some other equipment where 'scrubing' while steering was not a design consideration. It becomes even more complicated when you consider the idea that there are fine tuning aspects to ackerman geometry to affect low or high speed steering response instead of the mathematically correct setting (if there is one).

http://www.rctek.com/handling/ackerman_steering_principle.html

cyrusabdollahi - I don't think our poster is overly concerned about optimizing the car's tire grip on the road surface, as Danger mentioned we probably have less than 10 MPH to consider. And if the cart has a solid rear axle, steering geometry isn't too important to minimize front end tire scrubbing friction if the back axle is going to create a whole mess of friction at even the smallest amount of turn.

 

[Cyrus]

Thats a great link, thank you!

 

[dieselflight]

I was wondering if u could help me?

I am also involved in a science project in which I have to build a wooden cart but I have no idea how to power it, it must travel one meter as fast as possible and then stop before going to far over the line. Any ideas?

 

[Armandosworld]

Debating on which type of clutch to go with.

I am new to the go kart world and i am building one at the moment. I am a fast learner and have many hands on skills with many diffrent things including auto repair and custom welding. I started a frame from scratch and am now debating on the type of clutch i will use. In the last 15 min. on the internet i learned that there are a few if not many advantages of having a tourqe converter clutch. I have decided to go with it but just from what i have read. I was told today that having the main drive sprocket too close to one side on a live axel with an 8 horse briggs and straton will have some disadvatages and could pull to one side during acceleration and possibly twist my axel on hard take offs. IS THIS TRUE? Cause if so i would have to backtrack and move my engine mount more to one side. Its in the middle right now. I welcome feedback.

 

[Danger]

Welcome to PF, Armand. I can't really see that torque off-set would matter much with an 8-hp engine, but I'm not sure. One way to eliminate the problem, if you haven't already purchased the motor, is to use a vertical shaft version. That will put your drive line down the middle of the chassis. You just use a 90° twist in a V-belt to connect the axle.