# Modelling drag on a mesh analytically - Am I using a right approach

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Hi Guys,

I am trying to model viscous friction like seen in Karl Sims work on underwater virtual creatures.

I am therefore trying to model the drag forces of viscous drag on a mesh (with a rigidbody).

I can write an expression for the forces for a single point, and I have been using that in a simplified model, where I just have modelled the effect on a single triangle by using the triangles center and multiplied by its area. I model the drag from a triangle like this:

F_drag = -Dot(normal, point_velocity)*normal*some_constant

I have then applied the result on a rigidbody, by applying a position force onto my rigidbody. (I am using Unity3D by the way)

This works somewhat but I would like to do it a bit more detailed, so I have been attempting to integrate the expression over the surface of the individual triangles that make up the mesh. This presents me with two problems.

1) The first problem is that I can not just apply the result as a force on the rigidbody. Instead I think I need to write the expression as an effect on the velocity and angular velocity of the rigidbody directly. This has proven harder for me as it has forced me to look into how a force is transferred into these two values..I am currently working on this problem and I think I can make it work.

2) The second problem is that the expression I come up with turn very ugly when I integrate it. The way I integrate the expression is by expressing the force in the local space of the triangle and split the triangle in two triangles with a 90 degree angle. In this way I can write a double integral for each side of the triangle.

The problem this presents me with is that the expression contains a square root as the distance to the point has an effect on the resulting force. This makes the expression explode.

I am worried that I am approaching this in a wrong way and I am therefore on the lookoit for references for different approaches to solving the problem.

Currently im splitting the expression up solving it for the individual components. I wonder if there is a way to write in vector form and solve it in vector form, so it is not 6 isolated equations.

I assume this must have been done before by others more skilled than me, and I am therefore on the lookout for references to similar work.

Kind regards

Jesper Taxbøl

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F_drag = -Dot(normal, point_velocity)*normal*some_constant

That is the equation for pressure force, not viscous drag. That is, viscous drag is a tangential force, not a normal force as you have it. E.g., there is no viscous drag on an object perpendicular to the velocity, only pressure force.

Unless you want a highly complicated calculation, you're going to have to make some assumptions regarding the environment around the object. E.g., whether the velocity is in the turbulent region of flow for the fluid, whether the surface is close to another surface, etc.

Very generally speaking, for an object with a velocity in the turbulent region of flow for the fluid it's immersed in, the tangential force is proportional to the area, the tangential velocity of the fluid across that area, and the square of that velocity. I saw "very generally" because it depends on the shape of the object, not just a position on the object's surface. In most cases, there are areas of laminar flow (lower friction) and turbulent flow (higher friction).

For simulation purposes, you may want to start out with something like:

F = n * V2 * A

where:

F is the tangential force in the direction of V

n is a coefficient of viscous friction

V is the tangential velocity of the fluid across the surface

A is the area of the surface

I'm not familiar with Unity's physics engine but it sounds like it provides you the means to calculate the total force and torque on the body, through force-at-a-point.

For the above force, the result on the object's center-of-gravity is the force F and a torque proportional to F times the distance of the triangle from the CG. That is, it may provide you with the sum of the forces that will effect the object's velocity, and the sum of the torques that will effect the object's angular velocity. If not, you can sum the forces and torques yourself.

Edited by Buckeye

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