All bodies are roughly lumps of mass. All bodies carry mass. Mass curves spacetime, mass inherently is affected by INERTIA.
Inertia is a feature, a property of a body with mass (there are massless particles, but that is a whole new dimension of physics: Quantum Physics), and it is used to provide a measurement of a body’s ability to resist motion (from rest) or stay in uniform motion (velocity different (!=) from zero, acceleration equal to zero).
The more massive a body is, the higher its inertial properties are. That is true for a rock, that is true for an animal, it is true for a car and is true for an aircraft.
We can define a quantity called Linear Momentum, which is defined as p=mv, meaning, linear momentum of a body equals its mass times its velocity (in m/s). We can deduce and relate this quantity with Newton’s Law #2, but more importantly, we can define the Conservation of Momentum as a fundamental “rule” of this universe, and it is basically the Total Momentum of a System is the sum of the individual momentums of all its constituent masses and this Total Momentum IS CONSERVED AT ALL times.
Obviously, we must define what is a System, its frontiers, and therefore we must define which are the internal forces and which are the external forces. Internal forces of a system cannot change its total momentum. Systems which are acted by NO EXTERNAL FORCES are said to be ISOLATED. These conclusions are important to this matter.
Now, what does this imply?
You have 2 billiard balls. One is at rest, the other is moving towards it with a certain velocity. The total momentum of the system (these 2 balls) must be conserved if all external forces are discounted (external forces would be friction, and air resistance, for instance). When the magnitude of the impact and linear momentum are such that friction, resistances, etc, are minute by comparison, we can discount them (the margin of error is not much relevant). Continuing with the 2 balls analogy, the total momentum of the system is the sum of each ball’s linear momentum, in this case:
pTotal = pBall1 + pBall2
If ball1 is at rest, because p=mv, we have
pTotal = 0 + pBall2 = mBall2*velocity2
Now, the balls collide. When they separate, depending on the type of collision (elastic, inelastic) we can determine the momentum of each ball and also their kinetic energy (by the way, Kinetic Energy (KE) = (1/2)*mass*velocity^2, or 0.5*mass*velocity_squared).
In an inelastic collision, the total kinetic energy before the collision is different than the total kinetic energy AFTER. But momentum can still be CONSERVED, which implies we can consider collisions of automobiles and airplanes as events in which external forces are “irrelevant” and momentum is conserved.
Which means we can, given precise telemetry, know exactly how much energy is absorbed (and not recovered) during a collision.
Now, we have another quantity designated Impulse (I).
I = F*deltaT, meaning the impulse of a force is equal to the magnitude of a force multiplied (i.e.,*) by the amount of time the force is acting on a body (deltaT is the variation of time, or time interval: T_final – T_initial).
I = deltaP, with deltaP being the variation of P, which is Momentum (or in this case, linear momentum). Remember that P = m*v
So, on one hand we have I = deltaP, on the other I = F*deltaT
So, F= m*a, a is acceleration, acceleration is the variation of velocity (deltaV= vf-vi, i.e., velocity_final – velocity_initial) with time, so in fact F=m*deltaV/deltaT, with deltaT being T_final – T_initial), in effect giving us F= m*(deltaV/deltaT)
So, if I = F*deltaT, and F= m*deltaV/deltaT, we then have that (substituting F),
I = (m*deltaV/deltaT)*deltaT
The deltaT’s cancel each other out, and we then have
I=m*deltaV, which is the variation of Momentum (deltaP = P_final – P_initial). As mass is for the sake of the system wise calculations, immutable, we have then that what varies is the velocity.
All this to show you this result:
The impulse of the force of impact of a body into another can be precisely calculated. And even though we don’t know exactly the force of impact, we can calculate its impulse due to the other result (m*deltaV).
So, how does this apply to a tower and an airplane?
This way:
After the collision (fraction of a second later, or even a couple of seconds later), the tower remained at rest. Velocity of the tower (ignore the wobble, vibrations) is ZERO.
Velocity of the airplane is ZERO.
This is a purely inelastic collision, meaning we can calculate its momentum but we know that the kinetic energy of the system airplane + tower AFTER the collision is HUGELY less than right before the collision.
Here comes the mind-flash moment:
Where did all the energy go?
Well, fuel ignited. Enough? NO.
The towers buckled? NO.
So…?
The airplanes fragmented. All the energy was dissipated by fragmenting the airplane components and some tower parts (obviously).
Could an airplane survive the dive into a concrete/steel structure? No, but parts of it yes.
Could the nose survive intact?
I don’t see how. Really. The “skin”, fuselage of an airplane is roughly between 1.1mm (milimeter) and 2.2mm. A A320 is 1.1 to 1.2 mm, a B747-400 is at best 2.2mm, a military aircraft’s frame is as thick as 2.54 mm.
So, an impact of an airframe with a solid, heavy object at speed is destructive. For a big nose (large area) to cross unscathed tens of meters of truces, pillars, furniture, tubes, etc…is probably as likely as hitting jackpot twice on a national lottery.
Edit: Good work by the way.