Degrees and Angles

[Ross]

I usually use all the significant figures or decimal places available on my calculator - in this case ten.

 

When you get to a number that you are going to fly too or use in some way round it off to a sensible number of figures.

 

If that number has to be used for further calculations use all previously available digits unless you can see that it is not necessary. Recording of flight distances rounded off to the nearest mm is obviously going too far.

 

Like a planning sheet I would round up all distances to the next Nautical mile which will help with the safe calculation of fuel reserves required but might not help if you base future fuel consumption on the rounded up distance calculated.

 

In the case of computer calculated values special care has to be used by the programmer in setting up the calculation method in the original computer program due to the nature of binary arithmetic being used to calculate decimal numbers.

 

Quite huge errors can be introduced by believing the computer generated answer.

 

 

[Guest pelorus32]

My maths must be a bit out as I get 0.291m for 1km.I used 360*60 as the circumference of earth, giving a radius of 3434.747km, that equates to 0.017 degrees and 0.017deg for 1 km gives 0.291m. No allowance for refraction and I cannot remember the figures from my sailing days to work it out.

Now I know why I have such trouble landing, the strip is lower than it appears, at least that is my story and i am sticking to it.

G'day Ian,

 

I think you've halved the radius. The diameter at the equator is: 12,756.32 kilometers and a few kms less at the poles. As someone said it's a squashed sphere.

 

As to the question of how GPS copes with that: It uses a geoid which is an approximation of the shape of the earth. This geoid is fundamental to the WGS84 datum used by GPS.

 

Regards

 

Mike

 

 

[Guest pelorus32]

G'day Ross,

 

I thought that pythagoras was a sqrd + b sqrd = c sqrd where c is the hypotenuse.

 

The piece of trig you want is spherical trig which is explained here:

 

http://en.wikipedia.org/wiki/Spherical_trigonometry

 

You are right in making the distance of the sides the arc in degrees or radians. It's also a good reason to use nautical miles as there are 60 nautical miles in an arc degree of latitude at the equator or 1 nautical mile per arc minute of the same sort. It makes the maths quick.

 

You get to learn shperical trig when you learn celestial nav which in the old days required haversines to solve the triangles.

 

Regards

 

Mike