# Turn radius from forward velocity and turning velocity

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I have an entity that has a set forward velocity and set turning velocity. I was wondering how to get its turning radius; the radius of the circle the entity would traverse when it tries to go forward and turn at the same time. Thanks.

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what do you mean by set turning velocity ... do you mean a fixed angle per unit time, or a fixed amount of force per unit time, or something else?

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and the answer will likely involve arcsin / arccos etc - so you may want to look at those

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If something is turning at a radians per second, and it covers b metres each second, then its just a quick rearrangement of arc length

in this case b = radius*a, so that now becomes

So if it rotates 90 degrees each second, that is about 1.57 radians per second, and travells 8 meters every second, the radius of the circle it travells is 8 / 1.57 = 5.1 metres.

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