Here are three articles with full details about Total Lunar Eclipses and how to measure the Moon's distance and size, from The Classroom Astronomer magazine, Issue 5, December 2010. Shadow Cones. In Earth's Shadow. Caught! Shadow Reveals Moon's Size and Distance.
The Shadow technique can be done anyplace where the Moon can be watched through the beginning partial, total, and end partial phases of the eclipse. It can be recorded by drawing or photography.
The shadow of any spherical object in the solar system consists of a cone-shaped, dark central cone called the Umbra and an outer shadow zone surrounding the cone, called the Penumbra, where some sunlight shines directly into that space. The umbral shadow edges may appear sharp to the unaided eye but it isn't as sharp as it seems. This will cause some uncertainty in the measures, an important point all budding scientists should learn--no measurement is ever infinitely accurate. We are attempting to measure the diameter of the umbral shadow at the distance of the Moon when it gets eclipsed this time. The Moon's distance varies because of its elliptical orbit. The Earth's shadow also varies; the cone can be longer or shorter depending on whether we are close to the Sun or farther.
Courtesy Wikipedia Commons
A summary of what to do to measure the Moon using the Shadow technique:
Before The Eclipse
1. You MUST be within the zones where you can see all the total phases and at least some of the partial phases in order to do the Shadow Method.
2. Download the Moon drawing sheet and copy it to paper.
This is just an excerpt of the full sheet. See the upside-down three-toed footprint on the right (west side)? When you line up your drawings, that footprint should ALWAYS be to the right!
Print also the timeline sheet attached to the drawing sheet
and use or adapt this to another
piece of paper. The Moon moves its own diameter every hour so
each hour mark MUST BE wide enough to just appear on the left and right
edges of any Moon drawing image.
During The Eclipse
1. You must begin drawing the edge and coverage of the shadow on the Moon circles just before the partial phases begins and end after the partial phases ends. We suggest you make your observations every 30 minutes. Your drawings should draw the shadow edge as it appears over the lunar seas that you see with the naked eye (or low-power binoculars) and with the shadowed part shaded in. It is very easy and tempting to draw the eclipse as it appears in the sky relative to the horizon but this would be wrong!!! Observers should rotate their sheet of paper with Moon images to match the Moon as it appears, particularly as to which Maria (seas) are "up". Record the times of observations on a white part of the Moon circle. We suggest you NOT cut out the circles until after the eclipse.
(You can also take individual photos during the eclipse and print them and cut them out and put them on a timeline. There are some photographers who can take a series of photographs on the same image (sheet of film or stored CCD image and show the circular outline of the umbral shadow.)
After The Eclipse
1. Cut out and put the Moon drawings on the paper with the time line. Mark your hours and half-hours on the timeline as appropriate for your time zone. If you drew the Moon every thirty minutes you should have Moon images overlapping. This is a good thing, you will be able to "average out" some of your drawing discrepancies.
Note that though the Moon's features may appear to rotate as the Moon moves across the sky, they actually do not and all your lunar seas should always line up exactly the same way on the timeline - the seas that seem to form a three-toed footprint should always be on the right side of each drawing.
2. You should see that the edge of the Earth's shadow has a circular form, but you will only see part of the circle. Your next job is to make the circle that best fits the visible shadow edge arcs. This may require several attempts to get it done well; you are doing a BEST FIT and it won't be exact or going through all parts of the arc perfectly. We find that if you make tangents around the drawn large circular edge at several places, and then use a T-square to get perpendiculars to the tangent lines, you will find they roughly converse near a point. Adjusting your drawing compass in size and center location place, you will eventually find your 'best fit' circle.
3. Measure the
diameter of the moon image with a millimeter edge, and measure the
diameter of your best-fit shadow circle. Divide
the second value by the first; you should get a ratio between 2.5 and
3.0. Calculate the diameter in degrees of the shadow circle
by knowing the Moon is 0.5 degrees and multiplying that by the ratio
you just determined (e.g. 0.5 x 2.7 = 1.35)