Narrative: this section gives a brief overview of the story of how the fins were sized in broad strategy focused strokes.
Pre-cycle 2 research was done into optimal shapes and it showed that clipped delta and trapezoidal fins are often most effective shapes for our type of flight regime. After completing some OpenRocket simulations it was clear that clipped delta had better results.
Cycle 2 masses and lengths were significantly different than cycle 1.5 showing the need for in depth simulations again.
The team wanted to know what wind conditions we could launch in so the first study was to determine the effect of the wind speed we design for on apogee in the nominal condition. To accomplish this Spaceport weather was analyzed and simulations were run using last years fin sizing and cycle 2 masses, changing only the height of the fins according to the condition of required 2.5 calibers of stability in the various wind speeds tested. This resulted in the team targeting stability of 2.5 calibers in 9mph as it is a fair balance between apogee and stability at high winds. It is nice to note that the fins designed for 9mph are technically launchable almost up to 15mph as this is a very bad wind condition according to the weather data analysis.
After this there was a general feel of how various types of fin changes affect the vehicle and the focus changed to finding a good final fin design. In order to do this multiple fin shapes were designed that were believed to have a high chance of being successful and optimizing apogee. These were:
KOTS 2.0 shape
Tip Shape
Tip With Sweep Shape
Playing With Fire shape
A summary of why each was designed in their own way
KOTS 2.0 shape
Similar to KOTS a clipped delta fin has been found to be extremally effective in minimizing drag while having good stability, fin flutter characteristics, etc. This fin was required to become slightly longer and slightly thicker than the KOTS shape due to increased need for stabilizing and thicker due to increased speed which increases the risk of fin flutter.
Tip Shape
idea is to start with a KOTS fin and increase the tip chord to increase the resistance to fin flutter which allows for the fin thickness to be reduced which will reduce drag
Tip With Sweep Shape
Start with the tip concept and and add a sweep to move the fin CP effect back more in hopes that height can decrease and therefore thickness can decrease even more. Important to watch the weight increase from fin area increase
Playing With Fire
Idea is to take the current most effective fin and reduce the stability target to 2.0 calibers in 9mph wind to see how much apogee can be gained from this reduction in the margin.
Upon study it was not shown to have much of a significant improvement in apogee
Each of these shapes were then tested without changing weight of the fins using a variety of tests to ensure that under many team design changes (rocket mass, surface finish), or weather changes the fin would still be functional and to compare apogee in each of these cases.
Upon a first look it appeared that the Tip With Sweep Shape was the best considering a roughly 800ft gain in apogee over KOTS 2.0 however a calculation was done to double check the mass increase from KOTS 2.0 shape to Tip With Sweep Shape and this mass once applied decreased the apogee gain to around 300ft. Furthermore this reduced the stability to average closer to 2.3 calibers. To meet design target this then would require an increase in fin size (increasing mass) which in turn will require an increase in fin thickness (due to flutter) which further increases mass and cyclically reducing apogee. At this point it was clearly seen that the increase in performance initially though to be important was a result of not considering mass changes.
Therefore the final conclusion is that upon further confirmation the KOTS 2.0 shape is the best fin shape for LOTS. The remaining confirmation required is:
Confirm that with a new mass decrease in the engine there are not significant changes required/desired. Cycle 2.1 or 2.5 or something I think?
Confirm that the loading case does not require any changes to the fins. As loads have been working in parallel with simulations this is an very unlikely case.