(Disclaimer: engineering school dropout)
Flutter:
What’s the velocity range you’re looking at? For those of us operating normal
atmospheres, flutter is mostly an interaction between aerodynamic (speed)
forces and inertia. Every aerostructure has a flutter speed where that
interaction becomes resonant. Generally speaking, probability of flutter
increases with higher aero forces (speed), lower damping (stiffness) and longer
moment arms (fin CG further away from joint)
At a first order of analysis, something that propellant to mass ratio likely
won’t be moving fast enough to flutter an Al fin. I’m guessing M1.5 at max?
1/8th of an inch of Al moving at under M2 isn’t going anywhere, assuming that
the fin to case joint is good and stiff. People regularly hit M1.5 with 1/8”
plywood fins bonded with wood glue to an internal motor tube. You can hit M2
with 3/32” G10 fins surface mounted with nothing but a solid fillet of
RocketPoxy.
If you want to prove it to yourself, there’s FinSim and other similar programs
out there. You’re well within or better than the mainstream of mass, speed, and
materials used in garden-variety HPR.
Stability:
In general, you’re on the right track. It’s just a righting arm, and half the
force at twice the distance is the same arm. Fins further back is better.
You gain less than you might think putting shorter fins further back though
because your boundary layer is thicker than you might think, and you want the
fin to stick out into clean(ish), laminar(ish) air to provide that righting
arm. Cutting fin span by 20% might cut effective area by twice that.
The generally accepted practice is: trailing edge of your fin within a caliber
of the base, at least one caliber of span, and at least 2-3 calibers of root
edge. Take a look at fiberglass rocket kits in about your size range.
There’s two points you want to be looking at: off the rail, and the transonic
range.
Off the rail the figure of merit is ratio between your speed and wind speed.
Generally you want 1-2 cal of stability. Too little and you’re unstable, but
too much and you’ll weathercock into the wind. You can make off the rail less
worrisome by going faster. Since your T/W is fixed, solve this by having a
sufficiently long rail.
Transonic range: The bad news is that as a biprop pilot at burnout you’re
going to have max-forward CP and max-aft CG, which means your stability margin
will decrease as you fly.
At this point your CP is going to move forward. OpenRocket allows you to plot
CP vs speed or time. Unfortunately it won’t plot CG vs time, and in the case of
a liquid, CG moves back (bad) over time. While OR is generally useful, in this
case you might want to override your CG to max aft (no fuel, worst possible)
and ensure that you have 1.5 cal stability throughout the flight.
Trusting simulations:
You may also, time permitting, sim with RasAero as well. With as much time as
you’ve put into this rocket, it’s best to have two opinions. For a third
opinion, take a look at a Madcow or Wildman rocket in about your size range and
see if your fin size and placement is generally similar. Those are dead in the
middle of the envelope and make a good sanity check.
Feel free to contact me off list.
On Dec 29, 2018, at 7:44 PM, Robert Watzlavick <rocket@xxxxxxxxxxxxxx> wrote:
I've sized the fins for my 250 lbf biprop based on common guidelines I found
but I'd appreciate a sanity check. The rocket will be 14 feet long, 6 inches
in diameter and will weigh about 51 lb empty with a propellant load between
11 - 16 lb (10-15 second burn). I was planning on using four aluminum
trapezoidal fins with a 10 inch root chord, 4 inch tip chord, 6 inch height,
and 0.125 inches thick. From the flutter calculations in Apogee Newsletter
411, this should provide a 50% flutter margin at burnout. Is that reasonable?
The fin mounts allow position adjustment of a few inches in 1 inch increments
but I was considering configuring them for somewhere between 2 and 3 calibers
of stability. Is that a reasonable balance between stability and tendency to
weathercock? I plan to fly out of FAR on the Baxter rail but I'm not sure
what the typical winds are there.
When placing the fins to achieve a target Cp, is there a practical difference
between a taller fin closer to the CG vs. a shorter fin farther back? I
would think the aerodynamic moment would be the same either way for a given
set of conditions . Shorter fins farther back would be preferable from a
weight and drag standpoint.
I'm using OpenRocket for simulation and the results seem reasonable over a
wind range of 0-15 mph.
Thanks,
-Bob