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Wndsn Quadrant Telemeter Tutorials

Making the most out of our graphical telemetry computers.

Like with many complex instruments, there are multiple ways to solve certain problems and to measure the required inputs. Combining the various functions leads to a multitude of advanced uses.


Angular Size Explained

Level: Basic

Angular size is an angular measurement describing how large an object appears from a given point of view, according to the glossary.

Angular size is a relative term that does not say anything about the actual size of the object which is observed.

Angular size explained

Angular size explained. Note the relationships between the measuring plane in the top half and the Telemeter in the bottom half of the graphic.

Example

Imagine two different objects. Both measure at an angular diameter of about two degrees. Now, we know that they are both different in actual size. How come that they both appear as about two degrees in diameter?

The difference is their respective distance. The blue object in the graphic is much closer than the yellow one, yet both measure at the same angular size, as indicated by the dashed lines. Anything that fits tightly inside the dashed lines has the same angular size, while its distance is dependent on its actual size.

And that's the core idea of the Telemeter, knowing the angular size (α) and the actual size (S), we (or the nomogram) can determine the distance (D).

SOHCAHTOA helps evaluating the triangle, we need the tangent; opposite (S) over adjacent (D) and solve for (D) for the distance.

D = S / tan(α)

To summarize, we use (relative) angular size to get the (absolute) distance to or the height of an object.

Advanced Use

There is one useful value that we can derive from knowing just the angular size, and that is the relationship between the actual size of the object in question, and its distance. Thus, if an object measures at, e.g. 5.7°, we have a multiplier of ~10, calculated as 1/tan(5.7°). Therefore, whatever the actual size of the measured object is, its distance is 10x that value.

This makes recording angular measurements useful even if we don't have the object size or distance ready (still dependent on point of observation). An example would be a range sketch: Whenever we determine or learn either size or distance, we drop it into the equation and directly get the respective missing value.

D = S · Multiplier
S = D / Multiplier

Tycho can be used to experiment with these multipliers, without having to input actual size.

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