## Dynamic Analysis of 2 Air Vehicles Making Contact

## Dynamic Analysis of 2 Air Vehicles Making Contact

(OP)

I got assigned a problem where we have a vehicle attached by a cable floating along in the air (we'll call it the air tug). This vehicle has a catch bar angled downward to catch a small aircraft. The aircraft approaches the bar from the front (it has negative velocity in the frame of the air tug).

I am trying to find the force through the catch bar and the dynamic responses of the aircraft and air tug (rotational and 2D linear accelerations). I am assuming that the bar is acting like a 2 force member with equal and opposite forces (should be in pure tension).

I made free body diagrams for the air tug and aircraft which give 6 equations and 7 unknowns. To get 2 more equations, I made a closed loop vector of the positions and did the second derivative to get the acceleration relationship between the 3 bodies. With these equations I introduce another unknown but have 8 equations and 8 unknowns.

I put it in vector form and am trying to solve, but cannot get an answer to converge. I wanted to see if I am going about the right method for solving this problem, because I am stuck and cannot think of anything else.

Free Body Diagrams and equations in the attached slides

I am trying to find the force through the catch bar and the dynamic responses of the aircraft and air tug (rotational and 2D linear accelerations). I am assuming that the bar is acting like a 2 force member with equal and opposite forces (should be in pure tension).

I made free body diagrams for the air tug and aircraft which give 6 equations and 7 unknowns. To get 2 more equations, I made a closed loop vector of the positions and did the second derivative to get the acceleration relationship between the 3 bodies. With these equations I introduce another unknown but have 8 equations and 8 unknowns.

I put it in vector form and am trying to solve, but cannot get an answer to converge. I wanted to see if I am going about the right method for solving this problem, because I am stuck and cannot think of anything else.

Free Body Diagrams and equations in the attached slides

## RE: Dynamic Analysis of 2 Air Vehicles Making Contact

Also see "arresting gear" .

Mike Halloran

Pembroke Pines, FL, USA

## RE: Dynamic Analysis of 2 Air Vehicles Making Contact

## RE: Dynamic Analysis of 2 Air Vehicles Making Contact

From a statics point of view for a two force member (hook) the angle of the hook will be dependent upon a vector with:

Rise: Lift-weight

Run: Drag

Essentially if it is a two force member once hooked, the hook and Aircraft will swing upwards until this equilibrium is met. I suspect it will be near horizontal, as the aircraft should be capable of generating enough lift to lift itself (think glider)

If the hook is fixed (no rotation) to the airtug, then the hook IS NOT a two force member, and you need to take equation of equiplibrium about the hook.

Jeff

Pipe Stress Analysis Engineer

www.xceed-eng.com

## RE: Dynamic Analysis of 2 Air Vehicles Making Contact

what is Fcable on the tug ?

another day in paradise, or is paradise one day closer ?

## RE: Dynamic Analysis of 2 Air Vehicles Making Contact

Moving objects have kinetic energy, and when they crash, structures deform, converting the KE into Strain Energy. If the impact moves them relative to gravity or some other external force, then they also exchange Potential Energy.

That should add some equations to you system.

STF

## RE: Dynamic Analysis of 2 Air Vehicles Making Contact

This scenario is ‘similar-to’ several aerial scenarios, thus...

1. Aerial pick-up of a descending parachute [re-entry vehicle payload] or of a payload from the ground with a deployed/suspended balloon.

One system uses a trapeze system which is lowered from the back end of the aircraft [cargo ramp area] and hangs substantially below the belly of the acft. The aircraft ‘skims’ just above the parachute canopy or the balloon... ‘capturing it’... definitely a ‘sporty proposition

Alternately, a ‘scissor system’ on the nose of the aircraft [see C-130 scissor nose] captures the balloon or parachute. The pilot flies just under the parachute or balloon and the scissors closes rapidly on contact with the line entrapping the ‘cargo’.

NOTE.

These systems has been used to capture returning re-entry vehicles under parachutes with long suspension lines.

These systems have also been used for pick-up or cargo or humans from the ground, where NO runway exists... not my idea of ‘fun’.

2. Pick-up of an aerial banner from a ground site.

Low-flying tow-plane with a hook system drags the hook between 2 poles standing on the ground that have a wire-rope or synthetic rope strung between them leading back to the towed-banner which is in a ‘pile’. As rope the extends, the banner is rapidly ‘snatched-off the ground’ ‘ribbon-style’ [instant-to-instant getting heavier/draggier as the ribbon extends [banner lower-side is weighted so it tows up-right’].

NOTE. these ‘banners’ can be aerial gunnery towed targets; or towed banners for commercial advertising/promotion, etc.

3. Emergency arresting system for tactical aircraft.

A tactical aircraft [typically high take-off and landing speed fighter] deploys a tail hook which engages a wire-rope strung across the runway. On opposite ends of the wire-rope are long sections of boat-anchor chain, ends-turned-DOWN [each side of the] runway in the direction of travel. When the tail-hook engages the wire-rope it immediately begins picking-up the anchor-chain [both sides of the runway] and drags the chain in the direction of travel. Obviously the chain applies a proportionally higher drag on the tail-hook as the ‘dragged-chain length/mass increases as it follows the jet down the RW. These arresting systems have to be re-oriented whenever takeoff/landing directions change.

4. Aerial refueling systems.

4.1 Refueler-aircraft extends a male probe mounted on a trailing boom, which engages the internal [female] receptacle on an approaching receiver aircraft.

4.2 Refueler aircraft extends a long trailing hose with a [female] drogue which is engaged by the [male] probe of an approaching receiver aircraft.

NOTE.

System dynamics [‘antics’] in all these systems can become quite ‘sporty/sketchy’ unless heavily damped... especially in turbulence or significantly asymmetrical-conditions.

Regards, Wil Taylor

o Trust - But Verify!

o We believe to be true what we prefer to be true. [Unknown]

o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]

o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

## RE: Dynamic Analysis of 2 Air Vehicles Making Contact

That being said the interplay of the aerodynamic forces as the two pitch as a result of the impact makes it a bit less dull than the average two body problem. I imagine that works like a torsional spring.

Cheers

Greg Locock

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