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The data I have is:

Plane speed: 166.67 m/s

Mass: 170 metric tonnes.

Length= 50m

The plane penetrates 30 m inside the building before it stops.

I've tried two suggested solutions.

- Aceleration is constant. I use the classic equations:

F=m*a

a=a_0 (constant)

v=a_0*t+v_0 (v_0=166.67 m/s)

s=.5*a_0*t^2+166.66*t+s_0 (s_0=0 as I use the very moment of impact as reference for t=0)

Solving with the data:

v_final^2-v_0^2=2*a_0*s; a_0=(0-166.67^2)/2*30=-462.98 m/s^2

From velocity equation: 0=-462.98*t+166.67; Solving for t gives t=0.36 s (this is the impact time)

Equivalent Force:

F=170000*462.98=7870660 N

So the plane impact is equivalent to a Force of 7870660 applied during 0.36s. Using the software, it's equivalent to a "pulse": A horizontal line during .36 seconds.

Is this correct?.

After running the FEM sim, maximum deflection at top of tower gives 0.4 m, that I assume as correct, as the real tower swinged 0.6 m and after all simplifications of my model I think is close enough.

- Second solution: deceleration is linear (not constant). 0 at the moment of impact and maximum when the plane stops.

Our acceleration will be:

a=a_plane*t;(Assuming a=0 at t=0)

Integrating the expression we can obtain velocity and distance:

v=a_plane*t^2/2+v_0

s=a_plane*t^3/6+v_0*t

We know that at s=30→v=0. We also know that v_0=166.67 m⁄s . We obtain a non-linear two equation system. Solving it we obtain than a_plane=-4572.4188 m⁄s^2 and t=0.27 s. The plane stops at 0.27 s from impact.

The force we need to define in is:

F=m∙a=170000∙-4572.4188∙t=-7.773∙10^8∙t N, applied during 0.27s, gives a triangular shape in the software F-t graphic.

This solution gives a deflection of several meters, so it's not correct, but I don't see where I made a mistake.

The area of the graphics for both assumptions should be the same, but it isn't.

Any ideas?

Thank you very much.