# Trying to calculate the net force/torque of a rock climber on a wall

• I
• seedygrains
In summary, the conversation discussed a simulation of a rock climber on a 3D wall to visualize the free body diagram and how moving limbs affects the center of mass and forces on hands and feet. The group discussed the need for a numerical model of the skeletal linkage and potential complications such as friction coefficients and fatigue. The simulation is being done in VPython and the end goal is to possibly help with realistic film making or improving climbing skills.
seedygrains
Hey Everyone,

I am working on making a simulation of a rock climber on a wall in 3D space. The end result is to help visualize the free body diagram of the climber and show how moving your limbs moves your center of mass and changes the forces on your hands and feet.

I've been struggling to write the net force/ torque equations for this simulation and was hoping someone here would be able to help me out.

The question I'm trying to solve is this:

For a body with a known center of mass and 1-4 anchor points, what is the minimum magnitude and direction of the force required at each anchor point to keep the body static?

In the event that the equation is unsolvable (for example if there are only two anchor points and the center of mass isn't on the same vertical plane as the points) I would like to calculate the net torque on the center of mass.

Any help or suggestions on how to write these equations is greatly appreciated!

seedygrains said:
The end result is to help visualize the free body diagram of the climber and show how moving your limbs moves your center of mass and changes the forces on your hands and feet.
Welcome to PF.
I believe you will need a (numerical) model of the skeletal linkage, with each limb and the body having a centre of mass. The solution would be that of a dynamic 3D linkage, a structural space frame. The degree of freedom of the joints between the limb-links would be limited to match the human skeleton.

seedygrains
seedygrains said:
I am working on making a simulation of a rock climber on a wall in 3D space. The end result is to help visualize the free body diagram of the climber and show how moving your limbs moves your center of mass and changes the forces on your hands and feet.
Welcome to PF. Fun project!

What computer language and tools are you using for these simulations? What is your end goal -- Animations for realistic film making scenes, or helping elite climbers to improve their skills, or etc.?

The static FBDs are pretty straightforward, but there are definitely complications for transient simulations:
• Coefficients of friction between different surfaces (skin, rock, climbing shoes, etc.)
• Forces in jams (how strong are your hands and fingers?)
• Strength of arms and wrists and legs and feet in different moves
• Fatigue of the same...
Have you done similar simulations and computer animations for any other athletic moves in the past?

seedygrains
Baluncore said:
Welcome to PF.
I believe you will need a (numerical) model of the skeletal linkage, with each limb and the body having a centre of mass. The solution would be that of a dynamic 3D linkage, a structural space frame. The degree of freedom of the joints between the limb-links would be limited to match the human skeleton.
Thanks for the welcome!

I do have something like this so far, (see screenshots attached), I have a mass and position for each limb and use those to determine the center of mass of the climber.

I use the relationships between the positions of each joint and the lengths of each limb to control the motion of the body when you click and drag each part around (moving the hand moves the elbow which moves the shoulder, etc..)

Do you mean that I will need to know how forces move between the limbs in order to calculate the force on the hands? If we assume the climber can stay perfectly rigid, will that remove that need?

I was hoping we would be able to do this calculation using only the position of the center of mass and the positions of the hands/feet on holds

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berkeman said:
Welcome to PF. Fun project!

What computer language and tools are you using for these simulations? What is your end goal -- Animations for realistic film making scenes, or helping elite climbers to improve their skills, or etc.?

The static FBDs are pretty straightforward, but there are definitely complications for transient simulations:
• Coefficients of friction between different surfaces (skin, rock, climbing shoes, etc.)
• Forces in jams (how strong are your hands and fingers?)
• Strength of arms and wrists and legs and feet in different moves
• Fatigue of the same...
Have you done similar simulations and computer animations for any other athletic moves in the past?
Thanks for the welcome!

I'm doing the project in VPython. I haven't done anything like this in the past but I just started rock climbing and found out about VPython so I thought, why not :)

I do agree with the complications, at first I'm trying to just have the body grab holds assuming that the person is strong enough to hold themselves statically in any position. Once I get this far I'd like to add some more features in terms of being able to make a wall of different angles and allowing the user to choose from holds which have different angles, coefficients of friction, and sizes (which I'm thinking would affect % of body weight that could be supported)

The end goal for now is to show how changing your body position affects how hard you need to pull on the holds.

berkeman

## 1. What is net force and torque in rock climbing?

Net force is the overall force acting on an object, taking into account both magnitude and direction. In rock climbing, it refers to the sum of all the forces acting on a climber, including gravity, friction, and any other external forces. Torque, on the other hand, is the rotational force acting on an object. In rock climbing, it is the force that causes a climber to rotate around a specific point, such as their hand or foot.

## 2. How do you calculate the net force on a rock climber?

To calculate the net force on a rock climber, you must first identify all the forces acting on the climber, including the weight of the climber, the tension in the rope, and any friction or wind resistance. Next, you must use vector addition to determine the direction and magnitude of the net force. This can be done by breaking down each force into its horizontal and vertical components and then adding them together.

## 3. What factors affect the net force and torque on a rock climber?

The net force and torque on a rock climber are affected by several factors, including the weight and body position of the climber, the angle and direction of the climbing hold, the type of rock surface, and the amount of friction between the climber's body and the rock. Additionally, external factors such as wind and weather conditions can also impact the net force and torque on a climber.

## 4. How does the net force and torque affect a rock climber's movement?

The net force and torque acting on a rock climber can greatly influence their movement on the wall. For example, a greater net force pulling the climber towards the wall can make it easier for them to ascend, while a larger torque can make it more difficult for them to maintain their grip and balance. Understanding and managing these forces is essential for successful and safe rock climbing.

## 5. Can the net force and torque be calculated for every rock climbing scenario?

While the net force and torque can be calculated for most rock climbing scenarios, it is important to note that there are many variables that can affect these calculations. These include the complexity of the climbing route, the individual abilities and techniques of the climber, and the changing conditions of the rock surface. Therefore, it is not always possible to accurately calculate the net force and torque in every rock climbing situation.

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