# Projected waypoint

A projected waypoint is where a second waypoint is a given bearing and distance from a given waypoint.
Many GPS receivers can perform this calculation but for those that don't, here is how to manually calculate the second location.
And by manually we mean with a trigonometic table book or slide rule, pen and paper.

i.e. Your Laptop, PDA, mobile phone and calculator have flat batteries leaving only the GPSr working.

**Assumptions:**

This will only work for a few kilometers but should be fine for caching.
I'm assuming you are in Australia.

A book with sines and cosines or a slide rule and the ability to perform simple maths without a calculator!

You have printed this out and put it in your Geocaching folder!

**Given:**

Sorig is the first southing in the form dd mm.mmm

Eorig is the first easting in the form dd mm.mmm

D is the distance from location one to the second location in metres.

B is the bearing from location two to the second location in degrees.

S is the southing in the form DD.DDDDD, calculated from Sorig

**Solution:**

First lets calculate the distance in the southing and easting to the second location in metres.

deltaS = -D * cos(B)

deltaE = D * sin(B)

Now we need to convert this distance in metres to minutes of latitude and longitude.

deltaSmin = deltaS / 1853

deltaEmin = deltaE / (1853 *cos(S))

These are the variations to the minutes in the form mm.mmm

This is based on 1 minute of latitude 1nm. (1nm = 1853m)

The deltaEmin takes into account as you move towards the poles 1 minute of longitude gets smaller.

Snew = Sorig + deltaSmin

Enew = Eorig + deltaEmin

**Example**

*Sorig S34 46.533*
Eorig E138 36.090

D 800m

B 25 degrees

therefore S is 34.77555, cos(S) = 0.821

deltaS = -800 * cos(25)

= -800 * 0.9063

= -725m

deltaE = 800 * sin(25)

= 800 * 0.4226

= 338m

deltaSmin = -725 / 1853

= -0.391

deltaEmin = 338 / (1853 * 0.821)

= 0.222

Snew = S34 46.533 - 0.391

= S34 46.142

Enew = E138 36.090 + 0.222

= E138 36.312