Projectile Motion with a backwards Rotation/Tumble

[rg0ldberg]

I'm having a bit of a problem with some projectile motion. The standard motion is not a problem, but how to I compensate for a projectile that is rotating or tumbling backwards (nose over tail) at a significant rate of speed. The Tumble rotation is about 50 degrees/second on a cylindrical projectile that is about 59" long and 7.75" in diameter. The velocity is about 800feet/second with a launch angle of about 30 degrees.

I feel as though the tumbling will significantly shorten the flight path. I also feel as though the backwards rotation will impart a torque that steers the projectile to the right of centerline.

Appreciate any insight.

B/r

 

[berkeman]

Wow, that sounds like a hard problem. Do you have access to any simulation software that can handle projectile motion with varying air resistance?

 

[rg0ldberg]

Wow, that sounds like a hard problem. Do you have access to any simulation software that can handle projectile motion with varying air resistance?

Just my grey matter, the internet, and you good folks!

 

[ardnog]

My intuition tells me the mass of the object will be significant to the result.

I can't think of what you're trying to make. It sounds like the sort of projectile that is launched accidentally, like a vehicle explodes and an axle goes flying off. In a situation like that, the exact launch parameters are not well known, making the result of the calculation dubious.

 

[Lnewqban]

I would calculate the trajectory of the center of mass, around which the cylinder should rotate backwards.
Then, calculate the total flight time and how many radians of rotation the thing can achieve in that time: if comparatevily slow, the rotation may not be very influncial, other than added drag and some deviation from the vertical plane of flight.

 

[rg0ldberg]

My intuition tells me the mass of the object will be significant to the result.

I can't think of what you're trying to make. It sounds like the sort of projectile that is launched accidentally, like a vehicle explodes and an axle goes flying off. In a situation like that, the exact launch parameters are not well known, making the result of the calculation dubious.

The mass is about 400lbs...not making, just trying to locate =)

 

[ardnog]

So you are indeed trying to find something launched accidentally?

 

[A.T.]

I also feel as though the backwards rotation will impart a torque that steers the projectile to the right of centerline.

Why to the right?

 

[berkeman]

The mass is about 400lbs...not making, just trying to locate =)

Is this related to your car accident investigation thread from a couple years ago (which was closed)...?

Let's assume this is hypothetical...and may need to be in a different forum... but I am just looking for advice, maybe I am being too critical or perhaps not critical enough to get the proper inspections and repairs.

Assume my 2016 Chevrolet 1500 (2419kg) was struck by a vehicle of mass 1458kg. The situation was the right front quarter panel of the vehicle traveling approximately 40mph, no declaration prior to impact (<1.5s from impact to full stop), struck the rear driver's side wheel of my truck, not a glancing blow, direct impact. My truck was moving about 10-15mph as I had just accelerated trying to avoid the collision. I figure the force was about 17,000N (doing head math and I sustained a concussion so it's likely faulty)

My concern is that the impact from the vehicle to the rear wheel did more than cosmetic damage to the rim. The rear axel was binding when I moved from the road way into a parking lot, could have just been the brake caliper was stuck, but I am concerned, rightly so or otherwise, that the amount of force applied to the rear axel and suspension components was enough to cause premature failure of brakes, shocks, leaf springs, axel, or differential.

Thoughts?

 

[rg0ldberg]

Is this related to your car accident investigation thread from a couple years ago (which was closed)...?

No but thanks for thinking I am up to no good... =)
as stated trying to locate a projectile that took an unexpected path upon exiting a target. Foot search over a multiple square mile area has not been productive and trying to help the team narrow down the search grid.

was able to calculate exit velocity and angle from high speed video (2000fps) of the impact but the projectile has not been located.

 

[rg0ldberg]

So you are indeed trying to find something launched accidentally?

the test was intentional, the exit angle was unexpected.

 

[rg0ldberg]

Why to the right?

torque of the spinning mass...i guess it would have to be spinning quite fast to generate enough torque to significantly change its trajectory.

 

[berkeman]

as stated trying to locate a projectile that took an unexpected path upon exiting a target. Foot search over a multiple square mile area has not been productive and trying to help the team narrow down the search grid.

was able to calculate exit velocity and angle from high speed video (2000fps) of the impact but the projectile has not been located.

Wow, that's crazy! So you have video of the projectile going through the target, but it didn't impact the backstop as anticipated? How far away was the intended backstop (a hill or dune or something)? How far above the ground was the target? Was the projectile traveling horizontally at impact, or with some angle up or down?

 

[rg0ldberg]

Wow, that's crazy! So you have video of the projectile going through the target, but it didn't impact the backstop as anticipated? How far away was the intended backstop (a hill or dune or something)? How far above the ground was the target? Was the projectile traveling horizontally at impact, or with some angle up or down?

unfortunately there is no backstop, so items are visually tracked on exit, and usually quickly located with a foot search. I've tried to change this, and one day we will implement new tech like LIDAR to track the projectile. target is approx 40" off the ground, projectile traveling horizontally.
Normally exit is level flight. This is definitely anomalous.

 

[anorlunda]

It is indeed a difficult problem. If you could calculate how far it might travel without tumbling, that would be an upper bound. You might begin the search around halfway to that max.

The tumbling object might also deflect left or right. You said maybe right in the OP. No simple way to guess at the angle.

It might also skip after hitting the ground.

Can you use a drone to do an aerial search? If you're lucky, you may be able to see scuff marks where it touched the ground. Scuff marks would be most visible from overhead when the sun is low in the sky.

 

[jrmichler]

The standard motion is not a problem, but how to I compensate for a projectile that is rotating or tumbling backwards (nose over tail) at a significant rate of speed. The Tumble rotation is about 50 degrees/second on a cylindrical projectile that is about 59" long and 7.75" in diameter. The velocity is about 800feet/second with a launch angle of about 30 degrees.

I feel as though the tumbling will significantly shorten the flight path. I also feel as though the backwards rotation will impart a torque that steers the projectile to the right of centerline.

I suggest two simplifying assumptions:
1) It travels in a straight line (no torque to the right).
2) The drag is an average of the drag for a tumbling cylinder.

This drag plot is from Fluid-Dynamic Drag by Hoerner:

Based on this plot, I would try a drag coefficient of 0.6 with drag area 7.75" by 59" for the first calculation for the center of your search area. Then bracket it using drag coefficients of 0.5 and 0.7 to get an estimated diameter for the search area.

Reminds me of the time that a neighbor wanted to get rid of a 50 lb thrust model rocket engine by setting it on his back porch and lighting it with a propane torch. I persuaded him to at least point it up. He lit it, it took off, reached about 100 feet altitude at a 45 degree angle, made a 180 degree turn over my house to a path 45 degrees downward, then turned 45 degrees to a horizontal path down the center of the street toward a group of people, turned 90 degrees just before reaching the people, and disappeared in the woods. The whole flight took about a second. We never did find it.

 

[A.T.]

I also feel as though the backwards rotation will impart a torque that steers the projectile to the right of centerline.

Why to the right?

torque of the spinning mass...

That doesn't make any sense. Torque by what on what? And why would it steer to the right not to the left, since the situation is perfectly symmetrical.