Calculating Landing Loads from Sink Rate

[Burner21]

Hey there

Please excuse me if this is a bit basic, but it's just a quick question.

How would one calculate the vertical forces experienced upon a light aircraft upon landing, if I have both the sink rate of the aircraft and it's landing weight?

Appreciate any help, thanks a lot.

 

[Danger]

I'm not sure that you can, Burner. While I'm useless at any kind of math, I do know a bit about aeroplanes. The problem that I foresee is that just prior to touch-down you get into "ground effect". That can be quite unpredictable.

 

[JaredJames]

If you know the vertical component of velocity and the mass of the aircraft at landing, you can calculate the change in moment (from initial touchdown to no vertical motion).

Force is equal to change in momentum over time.

So F = Δp/Δt.

Where p = mv.

F = Δp/Δt = (m*Δv)/Δt = ma.

So by knowing the change in momentum and an estimate for touchdown time, you can come up with a rough idea for the landing forces.

It's a bit crude and as Danger points out, it's not going to be very realistic (far too many variables in reality for you to be accurate without some serious computing power).

 

[Burner21]

Hmm, I see what you mean. Any estimate for time will certainly be little more than a rough estimate and very crude at that. Ground effect wasn't something I'd really considered either, Danger, so thank you.

Simply put, I'm attempting to model the forces upon the landing gear of a light aircraft using a Finite Element Analysis package (ANSYS Workbench). I was just trying to get my head around the forces involved in a simplified sense, without compromising too much in terms of accuracy. I would then obviously apply these forces using the FEA package upon my model that I've constructed.

Do you have any thoughts on how one might do this to a greater degree of accuracy perhaps? As you've both pointed out, my original thoughts were rather basic!

Thanks again for your help.

 

[JaredJames]

You've gone from a 'basic' question to an FEA package. Blimey, there's a jump.

The principle is basically the same though, you need the forces involved. The timing isn't that crude, it's simply the time from initial contact to the aircraft no longer having vertical motion (that set of wheels is firmly on the ground).

Ground effect isn't actually a major issue as you know your sink rate (ground effect will alter that value, but if you have the value it isn't an issue). The bigger problems are things like sudden gusts or turbulence which could cause a heavy / not so straight landing. Increasing the load on the gear.

 

[Burner21]

You've gone from a 'basic' question to an FEA package. Blimey, there's a jump..

Ha, true. Initially I was just wondering about other peoples thoughts, but the responses got me thinking so I figured they'd be more useful if people knew more of the problem I was working on.

I agree on what you say about ground effect though, after reading more into it. To be honest I'd heard about it, but never really investigated.

I understand, but how would you calculate that time though? Would it take into account things like tire deformation, landing gear stroke etc? As only minor differences in that time would give rather large differences for the resultant force produced.

 

[AlephZero]

I understand, but how would you calculate that time though? Would it take into account things like tire deformation, landing gear stroke etc?

Yes, to calculate it from first principles you need to model the dynamic behaviour of the landing gear. You also need to allow for the lift from the wings reducing the weight on the wheels - and the lift will change as the a/c decelerates and rotates to put the nose wheel down, of course.

 

[Burner21]

I see, thank you for highlighting these factors that I had overlooked!

I have a copy of Airplane Design Part IV by Roskam which details how one would conservatively calculate the Kinetic Energy that needs to be absorbed by the landing gear upon touchdown. Is there any way to generate my simulation using this as opposed to force perhaps? Or would you say that my original instincts were more appropriate?

Thanks for your input, AlephZero. Greatly appreciated.