I saw this on the Grand Tour and here's another video of a severe case of axle tramp.
https://www.youtube.com/watch?v=BVQ5iZQTQJI
Why does this happen? Apparently, it is more likely on a vehicle with solid axles or worn out suspensions but I can't find a good explanation for it. I'd like to understand the physics behind what's going on.
In the States we call this wheel hop. Wheel hop is the rear axle loading and unloading itself in rapid succession. It's caused (as you stated) from either the design of the axle, worn parts, soft parts, hard tire sidewalls, or any combination of these.
Wheel hop is very common in vehicles with leaf springs and straight axles. This is because the axles tend to wrap the springs around the axle until the springs cannot be twisted anymore, then the springs cut loose and the wheel jumps off the pavement. Then the process starts all over again. Camaros and Novas from the last 60's and early 70's suffered from this. The way they solved this was to put something called traction bars onto the bottom of the axle at the springs pointing forward. This limited the flex of the springs, so pretty much eliminated the hop.
Mind you, it isn't just straight axle vehicles which fall prey to this. Even the newer Ford Mustangs with independent rear suspension (IRS) have this problem. In the link, they describe it as such:
Wheel hop is where the rear wheels will hop or sort of jump, but very quickly and violently, almost as if the rear end is going to fall out of the car. It only occurs during quick acceleration at the line as the wheels are trying to put the power down. Wheel hop is caused by the rear wheels being allowed too much motion in relation to the chassis and struggling to get grip.
Think of it like this. As you push the throttle, the wheels go into motion, but as the wheels move forward, the toe angle changes and you lost grip. As your Mustang loses grip, the wheels spin and your acceleration is drastically reduced which causes the wheels to go back to their original toe angle. The tires regain grip, and then the process continually repeats itself until you let of the gas or get out of the hole. It's a quick back and forth between accelerating and spinning the wheels which is caused by the change in toe angle, affecting the contact patch of the tires.
The reason it's bad for vehicles is it is very hard on the parts. Do it enough and you'll break something. Think of it this way, you're hammering the suspension parts over and over again in fast succession while this is happening. It's like using your car suspension like a jackhammer. You want smooth, straight power, and the car is giving you the ratty-tatt-tatt ... definitely not good.
