Relative Velocity Mental Maths Solution

• Jul 5th 2011, 01:49 AM
Relative Velocity Mental Maths Solution
Hi Everyone

I am not entirely sure that this question belongs in here, however most mental maths solutions regarding Relative Velocity involve trigonometry and so this is where I have posted it.

I think it is easier for me to post a problem that is similar, but to which I know the solution, before posing my questing to give some context.

eg. Two ships are travelling directly north at 12 knots. A bearing taken from one ship to the other reads 030. If either ship wants to open or close range on a steady bearing, then they need to steer left/right 6 degrees for every knot of speed advantage that they may have.

That is the simple mental maths solution for the problem, and I believe it is based on the Sine Rule.

My question is the opposite of this. Is there a mental maths solution to determine the course that would be required to come to, given that they have a specific speed advantage available and want to move a particular number of degrees around the circle, ending up at the same range from the ship?

Sorry this is a poorly worded question. I tried to create a drawing which better described it but was unable to do this computer.

Regards
Ian
• Jul 5th 2011, 03:38 AM
TKHunny
Re: Relative Velocity Mental Maths Solution
You do have to start with definitions. Do you know what "bearing" is?
• Jul 5th 2011, 08:17 AM
Re: Relative Velocity Mental Maths Solution
Quote:

Originally Posted by TKHunny
You do have to start with definitions. Do you know what "bearing" is?

Ok sorry.

Bearing - refers to the bearing of the object in degrees measured from true North, where 000 is directly true north and 180 is directly true south.

Knots - Speed in Nautical Miles (1852m) per hour, however provided the speeds for both objects/vessels are given in the same speed scale this does not matter.

Anything else?
• Jul 5th 2011, 02:24 PM
TKHunny
Re: Relative Velocity Mental Maths Solution
Yes, what's your plan for a solution? One is ahead of the other. Do we know anything else?
• Jul 5th 2011, 05:57 PM
Re: Relative Velocity Mental Maths Solution
Well in order to achieve this result, I would carry out normal relative velocity calculations, which involves drawing lines which represent speed and relative movement on circular graph paper and transposing these lines following rules in order to come up with an answer. I would also use RADAR to check this answer and update the solution.
I am trying to find out if there is a way to do this in your head without the drawing component, using mental maths.
I have an extensive powerpoint presentation on the rules and conduct of this style of relative velocity, however you are unable to attach powerpoints to this forum.

What we know is our course and speed, the other ships course and speed, our position relative to the other ship and a new position which we want to be in, relative to the other ship.
• Jul 5th 2011, 06:18 PM
TKHunny
Re: Relative Velocity Mental Maths Solution
#1 Why, since you have RADAR and computers?
#2 You may be able to exploit sin(x) = x for small values of x.
• Jul 5th 2011, 11:01 PM