A very simple memo: Focal Length (mm) = Distance (m) x Sensor Size (mm) / Subject Length (m)

Full-frame DSLR sensor is 36mm, APSC is around 23mm.

For example, photographing an aircraft taking off from an airport observation deck, Distance to Runway is 500 meters, using a Canon 5D4, the subject is a Boeing 787-9 airliner, with a length of 63 meters. So, calculate using the formula above. Note that it is best to leave about 10% margin on both sides for the length, 500 x 36 / (63 x 1.2) = 238mm

Therefore, you just need to use a telephoto lens with a focal length of 240mm.

Now, you might ask, how do I know how far it is from the observation deck to the aircraft? Here is a little trick. For example, look at an aircraft on the Apron, Stretch out your right arm and hold up your thumb, close your right eye, Use your left eye to observe the Boeing 787-8 in front of you. <img src=https://imgproc.airliners.net/photos/airliners/3/8/5/4569583.jpg?v=v4657470063b>

Then close your left eye and use your right eye to observe this aircraft, You can see the position of the thumb relative to the eyes has changed. If the thumb’s position has shifted by 1/3 of the aircraft’s length, We know this aircraft is 57 meters long, Therefore, the observation point has moved a distance of 57 / 3 = 19 meters. Then multiply this value by 10 to estimate the distance, which is 190 meters.

Returning to the topic of lenses, to photograph the aircraft above, 190 x 36 / (57 * 1.2) = 100mm So a 100mm medium telephoto lens is sufficient.

Finally, it turns out you don’t actually need to know the aircraft’s length to calculate the focal length. Distance (m) = Reference Length (m) x Relative Shift x 10 Focal Length (mm) = Distance (m) x Sensor Size (mm) / Subject Length (m) Focal Length (mm) = Sensor Size (mm) x 10 / 1.2 * Relative Shift

The simplified formula is: Full-frame DSLR Focal Length = 300mm * Relative Shift APS-C DSLR Focal Length = 192mm * Relative Shift

Let’s look at an example. If the thumb’s movement is 1/3 of the aircraft body length, Using a Full-frame DSLR, use a lens with 300 / 3 = 100mm focal length; Using an APS-C DSLR, use a lens with 192 / 3 = 64mm focal length.

If the aircraft is very far away in the air and the thumb’s movement is 3 times the aircraft body length, Then using a Full-frame DSLR would require a huge telephoto lens with 300 x 3 = 900mm focal length. (For APS-C DSLR, 192 x 3 = 576mm focal length lens)

This is a diagram from the New York Institute of Photography textbook from the 80s. The range of an 8mm lens is 180 degrees, The range of a 28mm lens is 75 degrees, The range of a 35 lens is 63 degrees, The range of a 50 lens is 43 degrees, The range of an 85mm lens is 29 degrees, The range of a 135mm lens is 18 degrees, The range of a 250mm lens is 10 degrees, The range of a 350mm lens is 7.5 degrees, The range of a 500mm lens is 5 degrees, The range of a 1000mm lens is 2.5 degrees.