Calculating surface normal vector

AI Thread Summary
To calculate the normal vector for surface F, the discussion emphasizes the importance of understanding the angle θ between the normal vector Nf and the velocity component U. It is noted that the normal component of U can be derived using the formula Ucosθ, eliminating the need for the absolute normal vector in certain cases. The conversation highlights that in a two-dimensional context, the normal vector can be determined by the negative reciprocal slope of the vector it is normal to, but specific coordinates or angles are required for precise calculations. The user seeks a formula for calculating the unit normal vector for surface F at a given angle, particularly in a Cartesian coordinate system. Clarification on the definition of surface F and specific examples is requested to provide a more accurate response.
andykol
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Hello,
I am trying to calculate normal vector for surface F Nf (see attached picture) to calculate velocity component for U. I tried to get more info but got confused.
Please tell me how I can calculate Nf.
Thanks in advance.
 

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  • Vector.JPG
    Vector.JPG
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Mathematics news on Phys.org
Welcome to PF!

Hello andykol! Welcome to PF! :smile:
andykol said:
I am trying to calculate normal vector for surface F Nf (see attached picture) to calculate velocity component for U. I tried to get more info but got confused.

I'm not sure what you're asking :confused: …

you don't need the normal vector …

to calculate the normal component for U, all you need is the angle, θ, between Nf and U …

the normal component of U is simply Ucosθ. :wink:
 
More information is necessary. In any coordinate system, a vector normal to another vector has a dot product of 0 with that vector. In 2 dimensions, this simplifies to the normal vector having the negative reciprocal slope of the vector it is normal to. you haven't given two-dimensional coordinates to the points, nor angles, so there is no way to calculate an absolute normal vector, but if the problem does not relate to any particular coordinate system (ie., there is no potential field; gravity, electromagnetism) then choose a convenient set of coordinates; ie., let that rectangle be horizontal with vertical sides; then the normal vector points along the positive x-axis. You still need the angle between F and N.
 
Thank you for reply.

But I need to calculate unit normal vector for surface F. I am looking for formula that calculates normal vector of surface with any given angle.
 
andykol said:
But I need to calculate unit normal vector for surface F. I am looking for formula that calculates normal vector of surface with any given angle.

Sorry, I still don't understand :confused: …

how is F defined?

do you have a particular example in mind?
 
Hello tiny-tim,

I have attached detailed picture. I have to calculate unit vector for surface-E Ne. For given Cartesian coordinates, how I can calculate surface normal?
E.g. 2D Cartesian mesh- I got surface-E at an angle θ.
 

Attachments

  • Vector.JPG
    Vector.JPG
    5.1 KB · Views: 674
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