# 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.

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

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.

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.

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.

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.