# How to calculate displacement from distance?

1. Dec 6, 2011

### otomanb

the distance from Islamabad to my hometown "sialkot" is 300km.
if i use helicopter what would be the displacement ?
Thank you!

2. Dec 6, 2011

### grzz

A map?

Or breaking it up into segments and estimating the displacement?

3. Dec 6, 2011

### JHamm

Checking google maps the displacement between the two is approximately 30km

4. Dec 6, 2011

### otomanb

i want to do it mathematically not using google earth.
is there any formula to find displacement from distance? suppose if i use helicopter how would i have to cover from islamabad to Sialkot?

5. Dec 6, 2011

6. Dec 6, 2011

### Naty1

I'm not sure what your terminology means....but a correct explanation for distance on the surface of a sphere is given here:

" The great-circle distance ....distance is the shortest distance between any two points on the surface of a sphere measured along a path on the surface of the sphere (as opposed to going through the sphere's interior). ..."

formulas are given in this text:

http://en.wikipedia.org/wiki/Great-circle_distance

7. Dec 6, 2011

### JHamm

There is a way to calculate displacement from the distance between two points because in normal usage the two are the same, the distance of your path isn't what most people would term the distance between the two points. And aside from measuring the two lines in your image and comparing them you aren't going to have much luck converting from one to the other.

8. Dec 7, 2011

### rcgldr

By distance do you mean chord length (a straight line between two points that goes through the sphere rather than along it's surface)? The wiki article linked to above includes the chord length formulas.

9. Dec 7, 2011

### Staff: Mentor

That looks like the best answer. Provided OP knows the co-ordinates of the two towns, just plug them into the round-earth formula, and he'll have their distance apart.

10. Dec 7, 2011

### mikeph

You can't calculate the shortest distance between two points if the only information you are given is the distance of a path between them. There is simply not enough information.

The least information you'd need is the bearing followed at every point on the path.