Casual reports of contrailing planes often include qualitative estimates of the height like:
"I just spotted a huge white plane with no markings - lower than other planes. It left thick white tracks that began between wing and tail of plane."
"At that moment a four engine jet flying lower than normal, estimated at below 20,000 feet, formed a thick contrail behind it."
It is often difficult to estimate the height of a plane because there are seldom any visual clues about size and distance. If it is heavily contrailing, the scale of the contrail (its width) can give a false clue. There are ways to estimate the height of a plane flying directly overhead provided the aircraft type is known. These are based on gross measurements in a photo of the wing span or fuselage length. See Ryan's Travels: The Chemtrail Conspiracy Theory (Misconception # 4).
Here is a more elaborate method. Some equipment and organisation are required.
Equipment required:
A good map of the area; scale 1:50000
Two people, each with a camera (or a theodolite) and a mobile phone or other means of communicating with each other
Vehicle(s) for transport
Method:
Field observation
On a day with contrail activity, position the two participants a good distance apart; 15 to 25 kilometres (10 to 15 miles) or more. This is the base line. Set up the base line so that the ground triangle (see Plan view below) is is more or less equilateral, and so that the photo will include the target and the horizon.
Pick locations that have easily identifiable landmarks in the distance. These will be used later to estimate angles in the photos.
Set the camera to take photos with the largest image size (assuming digital cameras are being used) for the detail.
Identify a plane or a feature of a contrail (start, stop, kink or curl) that both observers can see.
Zoom back with the camera to include the contrail feature and the horizon (not just the skyline) and at least one landmark.
Using the mobile phones, synchronise so that photos are taken at the same time.
If there is only one land mark in the photo(s), take another photo at the same zoom that includes the landmark in the contrail photo and 1 (or more) good landmark.
Return to base.
Evaluation of the photos, or equivalently, the angles measured by theodolite. Assuming there is only one baseline, proceed as follows.
(If there is more than one baseline, proceed separately with the set of photos from each baseline.
Upload the photos to a computer, or print them; whatever.
Organise the photos into two groups; those taken by observer "A", and those taken by observer "B".
Identify the pairs of photos that were taken (by the two cameras) at the same time.
Use the contrail/landmark photos, together with the map, to orient the baseline and obtain the angles between the baseline and the direction to the point below the contrail feature. Draw the triangle on the map or sketch it elsewhere, and note the length of the baseline and two angles.
This sketch illustrates the situation:
The angles and distances in brackets are to be calculated.
The Baseline distance AB is measured off the map. The angles A and B are also measured off the map (after identifying landmarks in the photo).
Angle C is equal to 180 - A - B degrees. (This can also be measured on the map as a check of the arithmetic.)
The distances AC and BC can be calculated using the Sine Rule for triangles.
AC = AB * sin(B)/sin(C)
BC = AB * sin(A)/sin(C)
AC and BC are the distances from the observers "A" and "B" to the point on the ground beneath the contrail feature they photographed.
Now obtain 2 elevations (angle up from the horizon) to the contrail feature from the photos of it by observers "A" and "B". Use the distance on the photo between 2 landmarks (and the angle between them from the observers position on the map) as a scale for this angle. This procedure is very sensitive to elevation so be careful. A longer base line helps here.
Using "completion of the triangle", 2 estimates of the altitude will be obtained (in units of the ground distance measurements).
This sketch shows the situation for observer "A":
The height above Observer "A" is AC * tan(A), where A here is the elevation angle.
The altitude of the contrail is the altitude of the observer plus its height above the observer.
The same can be done for the other observer. The difference between two altitudes should less than 2% of one of them. If they are wildly different, check the calculations, and that the photos were taken at the same time, and of the same contrail feature or plane or whatever.
Now convert the altitude to flight level. Convert from the distance units to feet, and divide by 100. The result, for normal jets, producing normal (or abnormal) contrails in temperate (midlatitude) climates, should be between 300 and 390, or thereabouts.
Handy Calculator:
Select what units are being used for the baseline distance, and fill in the required measurements (the wider text boxes).
If kilometres (statute miles) are selected, give the observers altitudes in metres (feet).
The calculator will evaluate after every change.
A Short Cut:
If it is known where the flight routes are (from the Civil Aviation flight route charts) and there is good confidence that aircraft stick to them (that is, they always take the same track across the sky), only one observer is required.
From photos taken from one observing place, it should be possible (using the map and landmarks) to obtain the sight line to the point on the ground directly beneath the contrail feature.
Measure this distance on the map, and enter it as the "Baseline distance AB".
Enter 60 degrees for both Angle A and Angle B.
The sight line distance to the sub-contrail point now appears in "Distance AC".
Now enter the elevation angle, and the altitude of the observation point.
Done!
(There is no need to use the "B" side of the Calculator when using this single observation method.)
Created: 05-Jan-2008 16:42:15 NZDT
Last modified: 09-Feb-2008 21:54:33 NZDT
