Can you make a Trebuchet that could launch a person one mile? Mathematically is it possible and how? As a bonus, how would you do it if you want the person to be alive after landing? (a question that came out of the design of the Trebuchet MS font)
5 Answers
Short answer: No. Certainly not without killing the human
Long answer: This is a pretty straightforward problem in projectile motion:
I'll design the hypothetical trebuchet for ideal conditions, i.e. there is no drag due to atmosphere. This is the best case scenario; things only go downhill from here.
Requirements of trebuchet: Fling human being 1600 meters ( I think better in the metric system)
Section 1: Speed
The trajectory of any object under the influence of gravity alone (no air drag) is a parabola. This parabola is uniquely determined by the velocity of launch, and the angle at which the person is launched. Such a trajectory looks like this:
![]()
V_(launch) is the velocity of the projectile (person) at launch
\(alfa) is the angle at which the projectile (person) is launched
h_(max) is the maximum height the projectile (person) attains
d is the distance that the person travels
h_(max) and d are given by the relations:
![]()
![]()
In our particular case, d = 1600m. To get the lowest possible (most efficient) value of V_(launch), the angle \(alfa) has to be 45 degrees.
putting that in to get the minimum value of V_(launch) we get:
![]()
Now, it is not this velocity per se which is a problem. In fact, Felix Baumgartner exceeded that speed by quite a bit in his record setting jump.
The problem is reaching this velocity with a mechanical device without killing the human in question. I shall elaborate:
Section 2: Acceleration
To get our human to the 126 m/s needed to travel a mile, we have to accelerate him/her from rest (Velocity = 0).
Using a uniform acceleration will be the gentlest possible way to launch the person. We are going to assume that the trebuchet is in fact a ramp angled at 45 degrees, and the human is accelerated along this ramp at a constant acceleration (that we decided) and let go once he/she reaches 126 m/s (think of a catapult on an aircraft carrier).
![]()
If we accelerate the person at a constant rate, the distance the person has to travel is given by
![]()
Now let us plug in some values:
V_(launch)^(2) = 16000 m^2/s^2
Let us be really gentle at first. We accelerate the person along the ramp at 1g = 10m/s^2. This is roughly the acceleration you will feel in a typical roller coaster
The height of this idealized trebuchet is, wait for it, 565 meters! For comparison:
![]()
Remember, since we are accelerating the person at uniform acceleration, this is the best case height. If we want to have an actual trebuchet while limiting the maximum acceleration to 10m/s^2, this trebuchet will be even higher.
Okay, that is not going to work. Let us get slightly serious. Let us launch the person at 5g, or 50 m/s^2. Using this value of acceleration, our trebuchet is 113 meters high. That is a 30 floor building.
Keep in mind, these are the accelerations faced by fighter pilots, and unless you actually train for these accelerations, you will certainly pass out due to cerebral hypoxia (not a great state to be operating a parachute in).
What if we want to specify the height of this trebuchet. Putting it at a reasonable value of 30 meters, we get an acceleration of 19g. That will certainly cause loss of consciousness in a person, and death upon impact with the ground 18 seconds latter.
So, in conclusion, any design of reasonable dimensions will kill the the person involved. You can stop reading here.
But, what about air drag?
Now things get complicated (and bad for our daredevil). We could apply models to approximate the reduction in range because of the drag on a flying human. But I will spare you the details. We will assume that in the presence of air drag, the person will travel to 10% of the distance that he/she would travel, had there been no air resistance. This is a very liberal assumption; humans are not very efficient projectiles.
To reach a distance of 1600m in the presence of air drag, we will have to shoot for 16 km. Revisiting the equation for V_(launch), we get a value of 400m/s. As Mikael Bengtsson rightly pointed out, this is supersonic. The person involved would be heated to a temperature of 115 degrees Celsius in flight.
Also, did I mention you need a ramp 1130 meters high to launch said person at an acceleration of 5g. To do it in a more reasonable height of 30 meters, the trebuchet would launch the person at 188g (person = pulp), requiring 60 megawatts of power at its peak!
Good luck.
Long answer: This is a pretty straightforward problem in projectile motion:
I'll design the hypothetical trebuchet for ideal conditions, i.e. there is no drag due to atmosphere. This is the best case scenario; things only go downhill from here.
Requirements of trebuchet: Fling human being 1600 meters ( I think better in the metric system)
Section 1: Speed
The trajectory of any object under the influence of gravity alone (no air drag) is a parabola. This parabola is uniquely determined by the velocity of launch, and the angle at which the person is launched. Such a trajectory looks like this:
V_(launch) is the velocity of the projectile (person) at launch
\(alfa) is the angle at which the projectile (person) is launched
h_(max) is the maximum height the projectile (person) attains
d is the distance that the person travels
h_(max) and d are given by the relations:
In our particular case, d = 1600m. To get the lowest possible (most efficient) value of V_(launch), the angle \(alfa) has to be 45 degrees.
putting that in to get the minimum value of V_(launch) we get:
The problem is reaching this velocity with a mechanical device without killing the human in question. I shall elaborate:
Section 2: Acceleration
To get our human to the 126 m/s needed to travel a mile, we have to accelerate him/her from rest (Velocity = 0).
Using a uniform acceleration will be the gentlest possible way to launch the person. We are going to assume that the trebuchet is in fact a ramp angled at 45 degrees, and the human is accelerated along this ramp at a constant acceleration (that we decided) and let go once he/she reaches 126 m/s (think of a catapult on an aircraft carrier).
If we accelerate the person at a constant rate, the distance the person has to travel is given by
Now let us plug in some values:
V_(launch)^(2) = 16000 m^2/s^2
Let us be really gentle at first. We accelerate the person along the ramp at 1g = 10m/s^2. This is roughly the acceleration you will feel in a typical roller coaster
The height of this idealized trebuchet is, wait for it, 565 meters! For comparison:
Remember, since we are accelerating the person at uniform acceleration, this is the best case height. If we want to have an actual trebuchet while limiting the maximum acceleration to 10m/s^2, this trebuchet will be even higher.
Okay, that is not going to work. Let us get slightly serious. Let us launch the person at 5g, or 50 m/s^2. Using this value of acceleration, our trebuchet is 113 meters high. That is a 30 floor building.
Keep in mind, these are the accelerations faced by fighter pilots, and unless you actually train for these accelerations, you will certainly pass out due to cerebral hypoxia (not a great state to be operating a parachute in).
What if we want to specify the height of this trebuchet. Putting it at a reasonable value of 30 meters, we get an acceleration of 19g. That will certainly cause loss of consciousness in a person, and death upon impact with the ground 18 seconds latter.
So, in conclusion, any design of reasonable dimensions will kill the the person involved. You can stop reading here.
But, what about air drag?
Now things get complicated (and bad for our daredevil). We could apply models to approximate the reduction in range because of the drag on a flying human. But I will spare you the details. We will assume that in the presence of air drag, the person will travel to 10% of the distance that he/she would travel, had there been no air resistance. This is a very liberal assumption; humans are not very efficient projectiles.
To reach a distance of 1600m in the presence of air drag, we will have to shoot for 16 km. Revisiting the equation for V_(launch), we get a value of 400m/s. As Mikael Bengtsson rightly pointed out, this is supersonic. The person involved would be heated to a temperature of 115 degrees Celsius in flight.
Also, did I mention you need a ramp 1130 meters high to launch said person at an acceleration of 5g. To do it in a more reasonable height of 30 meters, the trebuchet would launch the person at 188g (person = pulp), requiring 60 megawatts of power at its peak!
Good luck.
I doubt it: assuming no drag, the initial velocity has to be about 125m/s (280mph). Considering how much drag tends to slow things down - even if they go as slowly as a baseball and your modelling of the drag is as simplified as using a linear velocity dependence [1] - my money would be on:
The launch velocity would need to be significantly above the speed of sound.
[1] Trajectory of a projectile
The launch velocity would need to be significantly above the speed of sound.
[1] Trajectory of a projectile
As prior answers suggest, it isn't likely with an unaided human as the projectile.
However, putting the human in a vehicle of some sort may make it possible. The difficult part? Designing a glider with a glide path to go the distance that will also survive the necessary acceleration.
Or… make the trebuchet's arm a mile long. :-)
However, putting the human in a vehicle of some sort may make it possible. The difficult part? Designing a glider with a glide path to go the distance that will also survive the necessary acceleration.
Or… make the trebuchet's arm a mile long. :-)
I think you can. Here's how and why:
1. The catapult has to be big enough so that the swing/launch does not put too much G-load on the person.
2. It also has to have a gentle trajectory. A nice arc, with a relatively constant speed.
3. The person has to be an experienced BASE jumper. That has consistently opened and landed jumps less than 150ft in height. Insanely dangerous, but around here, they jump into a rock quarry on a regular basis.
4. Do your test jumps off a cliff to test. Then over water. Or the cardboard boxes.
5. Put it on YouTube. Collect the monies, retire early. Or if the person dies. Spend life in prison.
1. The catapult has to be big enough so that the swing/launch does not put too much G-load on the person.
2. It also has to have a gentle trajectory. A nice arc, with a relatively constant speed.
3. The person has to be an experienced BASE jumper. That has consistently opened and landed jumps less than 150ft in height. Insanely dangerous, but around here, they jump into a rock quarry on a regular basis.
4. Do your test jumps off a cliff to test. Then over water. Or the cardboard boxes.
5. Put it on YouTube. Collect the monies, retire early. Or if the person dies. Spend life in prison.
