1. Archimedes’ Principle

Archimedes’ principle states that the upthrust exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces. For our blimp, the aim is to achieve neutral buoyancy, whereby the upthrust exerted on the blimp is equal in magnitude to the weight of the blimp. This would allow the blimp to remain at a constant altitude in the air.

Equation relating the volume and mass of the blimp to achieve neutral buoyancy

We were able to calculate how much volume of helium we needed to generate enough upthrust to balance the weight of the balloon using the formula as shown above.

2. Moments about the Centre of Gravity

The turning effect of a force is known as a moment. The principle of moments states that, when a system of coplanar forces acts on a body and produces a state of equilibrium, the sum of the clockwise and anti-clockwise moments of the forces about any point in the plane is zero. To ensure that the blimp remains in stable equilibrium, we had to place our parts on the blimp such that the sum of moments about the centre of gravity of the blimp is zero.

We looked at the forces acting on the blimp while it is stationary in two planes, the Y-Z plane and the X-Z plane.

Possible outcome if y-Z moment is not 0 (view from the front)

In the Y-Z plane, we only have to consider the moments of two propellers on the blimp. As they are identical, they have the same weight, and thus they are equidistant from the Z-axis such that the resultant moment is zero.

Moments in the x-z plane from the different electrical components on V2

In the X-Z plane, we simplified our calculations by placing all the parts of the blimp in one plane (i.e. placing them along the centre line on the bottom of the blimp) so that we would only need to consider the moment of the forces experienced in this plane only. The diagram above shows the weight of the components and their respective distances from the blimp, such that the blimp is in static equilibrium. As the weights of all our components can be measured, we are able to obtain approximate numerical values for all 3 forces shown in the diagram. Additionally, d3 is fixed as it would be half the total length of our blimp. Hence, the only variables we needed to determine are d1 and d2, and this was done manually through trial-and-error as the curved and non-rigid bottom surface proved challenging for precise calculations.