Calculating the Feasibility of the Soccer-Bot

Date: June 20, 2018

Members Attending: Alexis, Kira

Mechanism: Fuel-Cube-Lift, Soccer-Bot

Todo: Decide whether to build or not

Before building a soccer bot, we wanted to calculate whether our motors are actually strong enough to slide the fuel-cubes for six metres.

First we did an experiment to find out the friction coefficient of the grass and the cube. For this we laid the grass on a tilted ramp. Then we slid down the cube. We then tested for the maximal angle at which the fuel-cube would stop sliding.

Sketch of experiment for calculating the friction

Instead of measuring the angle directly, we measured out the cathetes of the triangle and used the tangens to calculate the angle.

Calculating the angle

The force exerted by the friction is calculated using the force pressing the cube on the grass and the friction coefficient. The force pressing the cube on the grass is Fn as seen the sketch. The angle alpha between Fn and Fg (the force exerted by graviation), is the same as the angle of the tilted ramp.

From the sketch this mathematical connection follows:

Splitting the gravitational force into the forces tangential and normal to the slope

When the force of the friction (the one deccelerating the cube) and Ft, the force parallel to the ramp (the one accelerating the cube) are in balance, the cube doesn’t move.

Calculating the friction coefficient

Using the friction coefficient we want to find out, how fast the cube needs to be in the beginning to be able to slide for 6m.

The distance the cube travels is calculated by subtracting the distance calculated with the decceleration from the distance that the cube would travel with normal speed. The time the cube needs until it comes to a stop is quotient of the speed in the beginning in the decceleration.

Formula for the distance the cube travels, in dependence of the decceleration and the speed in the beginning

The decceleration can be replaced with the friction coefficient and the gravitational constant, as shown below.

Formula for the distance in dependence of the speed, the gravitational constant and the friction coefficient

We then adjusted the whole formula to calculate the speed needed in the beginning and put in the distance, the friction coefficient and the gravitational constant. The speed we need is 5.4 metres per second, which is about 200km/h. At this point we started doubting the feasibility of our soccer-bot idea.

Calculating the speed of the cube in the beginning

The next thing we wanted to know was how fast we’d have to accelerate the cube in order to reach the 200km/h. For this we assumed that we had a span of 10cm in which we would be able to accelerate.

Calculating the acceleration we need

We then calculated the force we need to exert, which follows from F = m * a. It was 14N.

Then we calculated the torque needed to be able to accelerate the cubes to that level using the 90mm traction wheels (radius of 45mm). With 0.63Nm the torque we need isn’t quite that great.

Calculating the torque needed

The next step was to calculate the rpm we need to reach a speed of 5.4m/s. The speed of the outermost part of the traction wheel is the circumference divided by the time the wheel takes for a full rotation. The angular speed needs to be 7.200rpm which is quite a lot.

Calculating the rpm

The last step was finding out whether our motors are strong enough to provide that much rpm and torque. Gearing them 24:1 would give us our desired rpm, but the torque would not be great enough. Thus our plan is not feasible, using two rotating wheels. However, by tensioning something and then releasing it, we might still be able to build a soccer bot.

Are our motors strong enough?

 

 

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