… while the rear button is still on the rail but after the fore button has released?

Recently there were several posts on DARS-General regarding a thought experiment by David Schultz about moving rail buttons to minimize perceived rotation caused by wind once the front rail button was clear of the rail. The proponents of the experiment surmised that the rocket was capable of significant rotation on the rail around the rear button and that moving the rear button forward closer to the CP would reduce or eliminate such rotation. A counter argument was made that no such rotation had been observed ‘in the wild’ by a group of experienced fliers and was likely not a real issue.

I was contacted by Jack Sprague of DARS off list to discuss this issue. I could not see the problem he and Dave Schultz described in spite of watching video of many take-offs in windy conditions. In all cases, rotation (weathercocking) did not occur until well after the rocket cleared the rail. I even pointed out Dave’s webpage at:

http://home.earthlink.net/~david.schultz/atacms/index.html

which shows his rocket leaving the rail vertically and then making a sharp turn into the wind. Dave’s own proposed solution to the severe weathercocking is to raise launch speed and avoid high winds.

It became clear that I was not going to make any headway against the thought experiment with empirical observations from photos or videos. So I decided to see if I could calculate how much a rocket would rotate while on the rail. I enlisted the aid of my son who is an Aerospace Engineering major at UT Austin. The results below are my interpretation of his suggested solution.

Jack had used an example rocket 1.6m long and had specified the CG, CP, and rail guide button locations. I added some additional information to allow me to do the computations involved.

Problem: using the following dimensions and information, compute rotation due to wind while the rear button is on the rail by itself.

* rocket of 1.6m length
* buttons at 1.1m and 1.6m from the nose
* CG of the rocket is at 1.1m
* CP is at 1.25m from the nose
* mass of 3.175kg (7lbs.), diameter of 7.62cm (3″)
* take off speed of 8.94m/s (20mph)
* cross wind of 6.7m/s (15mph)

from that:

* determine the amount of force the wind exerts on the rocket
* find the moment of inertia about the bottom rail button
* determine angular acceleration
* calculate the amount of rotation for the time supplied

Obviously a take-off speed of 20mph is well below NAR safety guidelines but was chosen to exaggerate the effect of wind. If rotation is an issue, this example should clearly show it. At 20MPH, the rear rail button is ‘unguided’ for .056 seconds.

A few simplifying assumptions were made. The surface area was determined as a rectangle, and a CD of .82 of the side plan of the rocket was chosen based on reference values on the internet. (A short cylinder with a aspect ratio of <7.) Force was calculated as F = A x P x Cd.

http://k7nv.com/notebook/topics/windload.html

The moment of inertia was calculated as a rod using I= 1/3 ML^2. (Using the formula for a cylinder gives a similar result.) This is a rough approximation, but good enough for illustration.

http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html#irod

The moment was computed using Force x rear rail button distance to CP. (As described by Dave Schultz in post 13426.)

Angular Acceleration = Moment / Moment of Inertia

Angular Rotation = .5 * Acceleration * time^2

finally, convert the answer in Radians to degrees.

For the example above, if the first button is located at CG, the rocket rotates .032 degrees while the rear button on alone on the rail. If you move the buttons to just forward of CG and the rear at CP, the time on rail is shortened, the amount of rotation drops to .008 degrees.

So in this worst case scenario the maximum you can reduce rotation is .032 degrees, assuming you can get it to zero. Moving the button closer to the the CP does reduce rotation, but primarily due to the shorter time the button is on the rail. As the rear button moves closer to CG or the center of the rocket, the moment of inertia actually drops – the rocket is EASIER to rotate on the rear button. But this is mostly offset by the shorter time on rail.

The force from windspeed rises as windspeed^2, so the amount of rotation in a 10MPH wind is only .014 degrees in this example.

Rotation is a result of time^2, so increasing launch speed from 20MPH to 30MPH to 40 MPH reduces rotation from .032 to .014 to .003 degrees respectively.

Under NAR safe launch speed guidelines, a rocket launched in a 10MPH wind should have a launch speed of 40MPH.

http://www.nar.org/pdf/launchsafe.pdf     (page 4)

This rocket would rotate .003 degrees with the rear button located at the rear of the rocket in those conditions.

The conclusion I draw from these calculations is that wind induced rotation about the rear button as the rocket leaves the rail is negligible even under extreme launch conditions. A take off speed of 20MPH in a 15MPH wind is a scenario not likely to be encountered in actual conditions, yet calculated rotation was only .032 degrees. Any increase in launch speed reduces the amount of rotation even closer to zero.

Dave Schultz can claim that he is correct – rotation is reduced due to the shorter time the rear button is on the rail.  But if the fore button is moved further foreword of the CG the rail must be extended to maintain launch speed. However the amount of rotation is so small that the practical effect is nil. As Dave clearly describes on his webpage linked above, the most reliable solution is to use a launch speed that ensures stability off the rail to counter the effects of the wind.

Of course it’s possible I’ve made an error along the way or used the wrong terminology. I’m sure someone will check my work and let me know if I’ve missed something. But it sure looks like leaving the rear button where it is normally placed is not going to cause any kind of issue related to wind.