Fin Cant Angle????

Is there any constraint or a mathematical equation to calculate the appropriate fin cant angle?

Clarification: canted how? As in other than perpendicular to the airframe? Skewed slightly to impart spin? Or the sweep angle on swept back fins?

I'm seeking 1) the angle between the root chord and the longitudinal axis of rocket tube (Cant angle) shown below


2) The sweep angle.

Further questions: what kind of application is this? High altitude, Mach+ speeds, general purpose fun-flying?

1) If you want it to fly straight with ~no spin, that angle should be zero.
1b) If you want to impart a specific rate of spin to it? That's going to be harder. The airflow will create a pressure field acting on the fin. You'd need to determine the resultant force through the fins centroid and calculate the torque moment it creates on the rocket.
1c) If you just want to impart some spin, 1-2 degrees should do it.

2)If its a sport rocket, sweep angle is probably just determined by whatever shape gives you a proper CP location (and looks good). If you're going high performance, smaller sweep angles tend to pop up because of fin flutter. Fin flutter increases when your finspan/average cord or Aspect Ratio gets larger. (look at the Madcow Super DX3 XL's fins as an example)

Also here's a cool link: https://www.dtic.mil/dtic/tr/fulltext/u2/a502110.pdf

I don't have any firm equations on hand, but 1-2 deg sounds good for a hunch. Too much cant and it'll be too draggy, although drag should reduce somewhat with roll rate.
If you were serious about canting fins, then you might want to consider stabilising your rocket with roll allowing for a 2 fin rocket. Although, that also makes rod/rail guidance tricky - probably required through the centre of the rocket.

Troy

The governing equations for something like this would be somewhat related to turbomachines, i.e. the fins are acting like turbine fan blades that generate power or torque, in this case to rotate the model rocket. Turbine design theory could be found in a college or graduate level engineering textbook. However, most of the typical design equations for rotating turbomachines usually assume a constant operating condition, i.e. RPM and inlet/exit velocity, or slowly changing inlet conditions, a model rocket goes through a large velocity range very quickly and the RPM would not be constant. But, you could consider maybe one design point at an average velocity during the boost phase and come up with a fin geometry to achieve a target desired RPM at some point during the boost. With too much fin cant angle it may produce so much aerodynamic force on the fins that they will pop off due to the combined forces of the wind and the rotation exceeding the strength of the materials. If the fins don't break off, if they were theoretically indestructible, a very large fin angle would introduce stall and increase drag, not sure what that would do, but would definitely increase drag and slow things down.

Considerations are similar to propeller theory, but the power is flowing from the fluid to the fins, rather than from the propeller to the fluid. One additional geometric feature that is commonly used in fans is twist. On a twisted blade the cant angle varies from the root to the tip to account for the different local velocity and relative wind, this is very apparent in airplane propellers and inlet compressor fans on jets. The tip is moving through a larger distance than the root and may need to be canted more than the root section to better distribute the aerodynamic load across the blade.

GlenP said:

The governing equations for something like this would be somewhat related to turbomachines, i.e. the fins are acting like turbine fan blades that generate power or torque, in this case to rotate the model rocket. Turbine design theory could be found in a college or graduate level engineering textbook. However, most of the typical design equations for rotating turbomachines usually assume a constant operating condition, i.e. RPM and inlet/exit velocity, or slowly changing inlet conditions, a model rocket goes through a large velocity range very quickly and the RPM would not be constant.

Click to expand...

What's more, strictly speaking it's a form of turbine, but it's not really close to a typical functional turbine where you're typically redirecting your axial flow via fixed nozzles and stators to impact your turbine blades face on.

Troy

FinSim will compute the forces and effects. It's a free download.