Benjamin James Glemminge Gordon, 18 år, Hafrsfjord
Skole: International School of Stavanger
Investigation into the Effect of the Number and Size of Fins on the Maximum Altitude Reached by a Model Rocket
A rocket can be defined as a flying vehicle powered by an engine, which ejects a self-carried propellant mass through an exhaust port. The key difference between a rocket and other flying vehicles is that it is a self-contained system, it carries all the components required to produce a force or thrust to move the vehicle. The advantage of this system is that rockets will work just as well without as within an atmosphere, and therefore make excellent vehicles to launch from Earth into space. A disadvantage is that rocket fuel or propellant is severely limited in supply and so burn times are short. By contrast, a jet engine requires an external supply of oxygen to combust its fuel, so will only function within the Earth’s atmosphere, but has a considerably extended powered flight time. The limited fuel supply available to a rocket requires that its flight be as efficient as possible.
Maximum altitude, or the apogee, of a vertical flight is a measure of the performance of a rocket design. For a given size of rocket and engine, the apogee will depend on its directional stability, and the aerodynamic efficiency with which it flies through the air. Model rockets use fins to provide stability during flight, keeping the rocket on track. Fins however are also a source of drag, which reduces flight efficiency. There is inevitably a trade-off between directional stability and drag.
This project investigates how the number and size of fins mounted on an otherwise identical rocket design affects the apogee attained and thus the efficiency of flight.
A series of model rockets were built and a payload bay constructed to carry a sensor package for recording flight data. Keeping the basic rocket and motors as identical as possible, two series of experiments were conducted:
Series1: The number of fins is varied from three to six. Shape and size are kept the same.
Series2: The number of fins is fixed at four, but five differing sizes of fins are used.
It was observed, in both series of flights, that the average rate of deceleration while coasting was greater than could be accounted for by gravitational attraction alone. This extra deceleration is due to drag. The equation for drag is given as
D=1/2*ρ* v2* Cd* A
(Where D = Drag, ρ = atmospheric density, v = velocity of rocket, Cd= Coefficient of Drag, A = cross-sectional area)
Using maximum velocity data, a theoretical, drag-free apogee was calculated for each flight, and compared with the actual “as flown” apogee. A technique was developed for estimating the effect of drag and a value of the coefficient of drag, Cd, derived.
In the Series 1 flights, a strong correlation was found between increasing fin count and decreasing apogee. Increasing the number of fins increased the cross-sectional area of the rocket, A, increasing drag and reducing the apogee attained.
In Series 2, the apogee decreased as fin size was increased. Although the cross-sectional area A, remained the same in this series of flights, the surface area of the fins was increasing and the additional drag this caused, reduced the velocity of the rocket and the apogee attained.
The 3M, “three medium” configuration flew highest and it is clear that the 3 fin configuration produced the best performance in terms of maximum altitude attained.
It is less clear what the optimum size is. The four “extra small” (4XS) fins were clearly too small and unable to maintain a stable flight direction. At the other end of the scale the four “extra large” (4XL) configuration, produced such a large amount of lift that it turned into the wind, like a weather vane, reducing the apogee attained.
To conclude on the best configuration, further testing is recommended with a 3S (three “small”) and a 3L (three “large”) design, and results compared with the best performing 3M (three “medium”) design.