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 = 25.48º So the whole camera angle = 25.48º x 2 Camera lens angle = 50.97º or ~ 51º 









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 ziptie 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 25.5º = (270 / 2) / altitude Therefore..... Altitude = (270 / 2) / Tan 25.5º 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 25.5º = (410 / 2) / altitude Therefore..... Altitude = (410 / 2) / Tan 25.5º Altitude = 429m or 1,418ft. 

