# Milestone 2 Calculations

I did up a neat excel sheet which allowed me to calculate some simple approximated values from a few given parameters:

Constants/Inputs Value Units
Gear ratio 0.333333333
kv 149
Input Voltage 28 V
Max Current 40 A
Mass of rider and kart 100 kg
Drag coefficient 0.804
Frontal Area 0.6 m2
How many motors? 2
Density of Air 1.225 kgm-3
Resistance of Motor 0.021 ohm

# Dependants

Derived Constants
kt 0.064089293
wheel circumference 0.319185814 m
Max power output 2240 W
Max Stall Torque 2.563571719 Nm-1
Graph Slope -0.000614471 Nm-1rps-1
At Standstill
Max Wheel Torque 7.690715156 Nm-1
Force exerted on ground 302.7840612 N
Acceleration @ Standstill 3.027840612 ms-2
@35kmh
wheel rps @35kmh 27.85211504 rps
motor rps @35kmh 83.55634512 rps
Drag @35kmh 23.35161459 N
Power loss @35kmh 207.5958537 W
Torque @35kmh 2.512228793 Nm-1
Power Output @35kmh 209.9126561 W

Since the power output of the motor is roughly equal to the fudged approximated power loss due to air drag of the kart at 35kmh, and given that the motor would definitely not perform at 100%, I can say that our kart will not even remotely hit 35kmh. I might be wrong though.

I actually secretly hope it does go above 35 =/

# Milestone 2

So given that we’re going to use two motors driving two rear wheels, we’ve done some calculations and we’ve realized that the kv of the motors we’ve been browsing are too damn high. The problem was that with the gear ratio given and the max speed that we’d be travelling at, the motors that we’re using won’t even be able to reach half of it’s no load rpm, which meant that the motors won’t be able to reach their peak power, which is at half of the no load rpm, and won’t be efficient, which only comes after peak power. And both power and efficiency are important.

The max gear ratio (to increase motor rpm) was also largely fixed to between 3-4:1. Even if we could buy any sprocket size we wanted, the sprocket would have to be smaller than the wheel we were using, and so eventually it didn’t matter anyway (since a larger wheel would accommodate a larger sprocket but would also need more torque to drive etc.). The smallest sprocket we could find for the motor had 12 teeth, and so that limited our options on the other end. We could design a custom gearbox to change gears/have a higher gear ratio, but we decided against this extra mechanical complexity and decided to go for a single speed (so we could also use can brakes).

We’ve therefore decided to go for an outrunner with the lowest kv we could find that was still within our budget, and this was it.

Following from there, since we already intended to buy two of those, we had to choose a controller for these outrunners. We looked around on kelly controller and found a cheap controller that was apparently on sale at \$59.99. We chose this controller because it could withstand a burst of 50A, and since we already intended to get a fourth battery, we could split the batteries between both motors to get a max current per motor of 80A (which we’d probably never reach anyway due to battery internal resistance etc.) Plus it came cheap, so it was perfect since we had to buy two of both the controller and the motor.

Budget check: 500-59.99*2-80.08*2-75=144.86

Woah. Depleting fast.

Since the sprocket size on the wheel didn’t really matter (it’d be the biggest the wheel would accommodate), we decided to go for small wheels so that we could have a smaller rotational inertia, and be lower to the ground (which we needed for handling issues).

After surfing about on McMaster we found a soft rubber wheel which already had a bearing for 13.18 each. Ouch. However, what attracted us was the flat surface and the apparently hard material used to make the wheel (both of which would help us when we wanted to attach the sprockets/brakes etc.).

Then followed a bunch of stuff like brake pads and ball joints and threaded rods and bronze thrust bearings etc. and we’re left with… 54.75!

And we haven’t even got to bolts and nuts and brakes and aluminium rods (for steering). Oh dear. Regardless, the BOM is here for your viewing pleasure (whoever you are):

# Choices choices…

And so our lordcommander instructor Charles told us that a differential would be too ambitious a project in such a short timespan. Somehow or another he was extremely convincing, so we agreed to not make the most awesome electric go kart under 500 be so ambitious. So here are some of things that we’ve decided on:

1. Four Wheels
2. Around a 1-5 Gearing
3. Probably going for four battery packs
4. Two BLDC motors and two kelly controllers

Steering hasn’t been decided on yet but we get the feeling we’re gonna be able to hodgepodge it later on into something beautiful.

The reality is that our kart is now going to look very much like the chibikart except probably much bigger, because we like more leg room.

Even the braking system is probably gonna be similar (a brake pad on the outrunner) because of the added complexity of having to add a brake disc on top of a sprocket onto a wheel.

But then again imitation is the highest form of flattery =/

# Preliminary Brainstorming and Sketches

Based on the briefings and the 2.007 blogs that we’ve seen, there are a few variables that we could explore:

1. Differential?
2. Gear box?
3. How many wheels?
4. And also how many motors?
5. Big or small wheels?
6. How is steering done?

# Differential Disassembly

We found a cheap differential and we thought we’d disassemble it, just to learn more about them so we could decide better if we wanted to construct/buy one (the one we could order was almost the exact same thing from Surplus Center).

it was an extremely simple design, but at least we learnt sort of how much material to expect, how a simple bevel differential works etc.

# And So It Begins.

“Those who assume hypotheses as first principles of their speculations… may indeed form an ingenious romance, but a romance it will still be.” – Isaac Newton, Principia Mathematica