# Calculating laterel acceleration from change in direction (bearing)

Hi all,

Ive made a car simulator for a uni project, i am now trying to calculate lateral acceleration (Gs) for the car.

It models a car going round a track, however the track is made up of a series of straight lines, no curves. curve (type things) are achieved by a series of straight lines close together.

I need to calculate the lateral acceleration from the car changing from one direction to another (essentially instantly but more likely effectively over a very short period of time.

Ie the change from going on a bearing of 50deg at 50mph and changing course to 60deg still at 50mph will exert some lateral Gs. But how can i calculate how much?

There is a formule for the radius of a circle, as in if the car were going round in a circle:

R^2/ speed gives lateral accel but i have straight lines, no curves.

Ive looked at making the lines give an effective radius but that isnt working too well.

Any help would be SO much appreciated. there is clearly a link between a change in direction (ideally in degrees) and lateral acceleration but i cannot find a formula.

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If a car actually changed direction in zero time, the G force would be infinite because the corner where 2 straight lines meet has zero radius.
You need to get a non-zero radius at the corner. Then you have a piece of a circle and the centripetal G-force is easy to calculate from the standard formula.

yea, true, i see that if there is an "instant" change in direction there will be effectively infinite acceleration.

If the change were to go over one unit of distance as opposed to an instant change is tehre a way that there is a formula to calculate the acceleration with the direction in degrees and the speed. Is this possible if there is a change in one one unit rather than instantly.

Cheers

See below

/ <<< 10degree
/
/
/
. <<< point of change (one unit of length)
|
|
| <<< 0degree direction
|

I understand your diagram, despite the absence of tabs. Have a look at the pic I've attached. Assume your car is travelling on a circular arc while turning. As soon as you have the radius, the answer is easy.

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Yes, appologies for the lack of tabs, clearly my spaces didnt make the formatting. Glad it makes sense though :)

Yep, id come accross the paradigm of finding the radius of a circle that would intersect 3 points on the lines (say one where the two meet, the other two a bit along the respective lines).

This brings me to the question of whether there is a way to calculate the radius of the circle from the angles of the lines. i ask this because the way ive coded the app its very difficult to find points on the lines as theyre drawn in real time.

I may seem obsessed with the "bearing" and its relevance but it just seems there should be some direct correlation between the circle radius and the change in bearing/heading.

Hope that helps show what im looking for, if it exists :)

Earlier you suggested that the change takes place in a unit of distance.
Have a look at the pic. You can choose your circle so the section of arc I've labelled 'A' has length 1. The paths intersect tangentially with the circle.

You're designing the road, you can decide the tightness of the corner.

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Hi Andy

Nice to see another student doing a car simulation for University. I'm curious as to what aspect you are looking at with your project?

I've just added lateral calculations to by project, I came across this thread while googling for the formula. A bit late now after a month and was probably a typo anyway but:
R^2/ speed gives lateral accel