The Punishing Physics of Your Favorite Ninja Warrior Stunts
Maybe in the future, there will be more official competitive sports that look like Ninja Warrior—that would be cool. If you haven’t seen the show, you could say it’s just an adult-sized obstacle course for humans and ninjas.
But besides being a fun event to watch, Ninja Warrior is also a great source of physics lessons. Here are my favorite physics examples from the show.
Conservation of Momentum
At the end of the pipe slider, contestants need to leap from a sliding bar onto a landing space.
What makes this obstacle so difficult? The answer is momentum. Here is one of the most fundamental ideas in introductory physics—you need a force to change an object’s momentum. The ninja wants to increase his horizontal momentum so that he will make it to the landing pad. In order to increase horizontal momentum, he needs a horizontal force. What force could push on the human? Well, the bar could push except that the bar slides with very low friction. That’s the problem.
As the human swings forward, the pipe swings back. It would be like jumping off a low mass boat. When you push on the boat to increase your momentum, the boat moves back. Yes, this is the same thing as saying the center of mass stays in the same place.
Friction Running Up the Warped Wall
Could you have a Ninja Warrior first stage without the warped wall? I don’t think so. The basic idea is for the ninja to get to the top of this wall (the new one is 14.5 feet high). It’s clearly too high to just jump so you have to do a combination of running up the wall and then jumping.
You shouldn’t be surprised that this obstacle also deals with forces (it’s a physics post, remember). As the runner moves into the wall, there is a change in velocity (even if it’s just a change in direction). In order to change velocity, you need a force.
There are essentially three forces on the human in this move. There is the gravitational force pulling down, the wall pushes back (to the left) and friction pushes up (parallel to the wall). The frictional force depends on how hard the wall pushes back on the human. In order to make the wall push back on you (to create friction), you would need to change your velocity. You can do this by going at the wall really fast and then pushing yourself away. Of course, if you push too hard you won’t be in contact with the wall anymore. Really, it’s a tough situation. On top of that, at some point you need to jump to reach the top lip of the wall.
Actually, there are two parts to this obstacle. First you have to jump into two vertical parallel walls and use your hands and feet to support yourself. Second, you need to alternate between hands and feet to move through the obstacle.
Let’s just look at the forces need to keep a human from falling while in the spider walk. Again, it involves friction. Here is a force diagram that might help.
The total vertical force has to be zero in order to prevent the human from falling. How do you increase friction? Yes, you push harder on the wall. This wall pushing becomes problematic when your legs aren’t very long. If you have to do a split just to reach the wall, you aren’t going to have a good time.
Whoever invented the spinning log obstacle must not like humans. This thing looks super tough (which is an order of magnitude more difficult than just “tough”). The idea is to hold on to this cylinder as it rolls down a ramp.
Here is the deal—when an object moves in a circle, there is an acceleration. The direction of this acceleration is pointed towards the center of the circle and the magnitude of this acceleration depends on both the angular velocity (ω) and the radius of the circle.
As the log rolls down the incline, the angular rotation speed increases. Notice that the acceleration is proportional to the square of the angular velocity. So a double in angular speed quadruples the accelerations. This acceleration means that there must also be a force pushing the person towards the center of the log. Of course this force is provided by the person’s grip—but how hard do you have to hold on? Let’s say that the log rotates twice every second with the human at a 25 cm radius. This would be an acceleration equivalent of about 8 g’s. Yes. That’s why it’s hard to hold on.
This is another iconic Ninja Warrior obstacle. The warrior must do a pull up on a bar with enough speed to be able to move the bar up to a higher rung.
With a normal pull-up, you need to increase the center of mass which increases your gravitational potential energy. For the salmon ladder, you need to also end the pull up with enough speed that you are launched up. You need to have enough time off in the air to move the bar from the lower rung to the higher rung. This means you need to increase your kinetic energy.
Increasing both your kinetic energy and your gravitational potential energy in short time means that this will require power. How much power? Based on a previous estimation, I get anywhere from 700 to 1200 watts.
Only a true ninja could produce this kind of power (even for a short time). That is why I’m not a ninja warrior.
Follow this link: