# Modelling an Airplane Landing?

1. Mar 10, 2012

### pige

1. The problem statement, all variables and given/known data

Working on a project for a vibrations course, task is to quantitatively analyse a system in which mechanical vibrations occur. I chose to model aircraft landing gear, for a variety of different airplanes, namely one large transport (747), a simple tricycle gear GA plane with cantilever suspension (Cessna 172), and either a taildragger or else another trike with an oleo type shock absorber.

2. Relevant equations

I was planning on modelling the system as a non-homogenous second order differential equation, with the forcing function being some sort of impulse or sum of impulses (possibly using the Dirac Delta function or a convolution integral, but I still need to work that out). However, I was wondering if anyone would be able to help me to figure out or derive parameters such as damping ratio, equivalent spring constants, and also how factors like Weight and Balance, would affect the system response. I plan to do some quantitative analysis in matlab for this project, and what I would ultimately like to be able to do is to generate data and plots for maximum passenger acceleration and also gear displacement as a function of time.

2. Mar 17, 2012

### OldEngr63

Just a few questions for you to think about.

1. Before touchdown, the aircraft in the air has 6 rigid body DOF, in addition to all the many vibratory DOF. This is true for all of your three air craft types. Even on the ground, moving, it still has 6 DOF if we allow for the fact that the tires and shocks offer significant vertical motion, and all other motions are almost as free as they were in the air. How then do you propose to reduce this to a single second order (1DOF) system?

2. Might it be a good idea to specify in advance what part of the aircraft motion you are going to attempt to model, say perhaps the heave and pitch following touch down? Or will you be more ambitious and try to model things like the yaw motion? or the possible flutter of the nose wheel? Just how far are you going to attempt to go in your model? It would seem wise to spell out your goals in advance, otherwise you will never know where you have met them or not.