Measuring Flying Altitude


This page details one method for calculating flying altitude using an aerial photograph.

For best results the camera was mounted pointing directly down from the plane fuselage. This would provide mapping shots removing any error due to perspective.

Mapping photo

 

 

 

 

 

 

 

 

First the lens angle of the camera had to be established by taking a photo of a known dimension from a known distance.

In this case the garage door was photographed from a distance of 3 meters. The garage door was 2040mm in width. This equated to 1609 pixels in the photo.

 

 

 

 

 

 

 

 

To work out the camera lens angle, the width of the whole frame would need to be known in meters. This was calculated using the ratio of Pixels and mm's.

We know 2040mm = 1609 pixels

Therefore....... 1 pixel in this photo = 2040 / 1609 = 1.26mm

Picture width in pixels was 2270.

So......... 2270 x 1.26mm = 2860.2mm actual width across the whole frame.

 

 

 

 

 

 

 

 

Next trigonometry was used to calculate the lens angle.

The green line on the diagram was added to create a right angled triangle with a base of half the frame width and a side of 3000mm long.

So half the camera angle would be

Tan Angle = (2860.2 / 2) /3000

Tan Angle = 0.4767

Therefore Angle = 25.48

So the whole camera angle = 25.48 x 2

Camera lens angle = 50.97 or ~ 51

 

 

 

 

 

 

 

 

Finally to calculate flying altitude the actual distance between objects on the ground would be needed. To measure this a simple measuring wheel was used made from a bicycle wheel as shown. The wheel had a zip-tie which 'pinged' a bell each revolution to make counting easy.

Measuring wheel with audible counter

The circumference of the tyre was found to be 1255mm

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

Click to enlarge

In this first photograph the distance measured on the ground was between the two end white lines shown.

This distance was 166 turns of the measuring wheel.

166 x 1255mm = 208330mm

Again this would need scaling up to the whole frame to allow the calculated camera angle to be used.

208330mm = 1751pixels

so 1 pixel = 208330 / 1751 = 118.9mm

Frame size = 2270 pixels; so actual ground width in photo frame = 2270 x 118.9 = 270m

 

 

 

 

 

 

 

 

The height of the plane could now be calculated using triangulation and scaling.

Again a vertical line was added to create a right angled triangle with a base of half the measured length, so half the angle was also used.

Tan 25.5 = (270 / 2) / altitude

Therefore.....

Altitude = (270 / 2) / Tan 25.5

Altitude = 283m or 934ft.

 

 

 

 

 

 

 

 

In this second example the plane looked significantly higher - about as high as could be flown without losing sight of it.

Click to enlarge

The ground distance between these next 2 point was 222 turns of the measuring wheel.

222 x 1255mm = 278,610mm

Scaling up to the whole frame gave :

278610mm = 1543 pixels.

So 1 pixel = 180.5mm

Frame size = 2270 pixels; so actual ground width in photo frame = 2270 x 180.5 = 410m

 

 

 

 

 

 

 

 

Tan 25.5 = (410 / 2) / altitude

Therefore.....

Altitude = (410 / 2) / Tan 25.5

Altitude = 429m or 1,418ft.

 HOME

 

EMAIL

 

RC Flying