Calculating Dimensions, Timings, Ratios and Angles

CAUTION: Compromise Ahead
I will describe methods I used to determine dimensions, ratios, timings, angles, etc. These methods can be as accurate as you wish to implement. The calculations will allow you to be as accurate as possible, however I am building a visual telescope, not a photographic telescope. As such, I can be a little more relaxed in my implementation of dimensions. I am also a casual observer. As such, I know I will not spend more than 10 to 15 minutes observing any particular object. This allows me to be even more relaxed when deciding how to construct my telescope. Here are a few compromises I will make knowing that it will not be precisely correct:
I align on Polaris, not the true celestial north axis.
I do not motorize the declination bearing.
I use one revolution per day (1 RPD) as the basis of my drive mechanism, not true sidereal time.
I rely on friction to compensate for exact balances.

CONTENTS
Angle of Polar Axis
Drive Construction Variables

Angle of the Polar Axis (Northern Hemisphere)
In order to align the telescope so that it can track objects in the sky, you must use one axis of rotation to align along the ecliptic. A normal ALT-AZ mount that uses elevation and azimuth, becomes an EQUATORIAL mount that uses declination and right ascension. When aligning an equatorial telescope with the ecliptic, the polar axis ANGLE must be determined. This is very easily done by using your latitude. Therefore, I will set my polar axis at 45 degrees because that is the latitude of Minneapolis, where I live. In order to compensate for different observing sites at different latitudes, I will raise or lower the polar bearing of my scope by a few degrees.

You can find your own latitude by searching for your city at the following web site: Atlas Query - Astrodienst
I realize that this is a site about astrology, but it has the best free worldwide latitude finder I've seen. It also includes time zone, a world map to reference as well as the current local time and Universal Time; so please, no lectures!

For my friends in the Southern Hemisphere, I apologize. I have NO experience in aligning telescopes south of the equator. If anyone has suggestions or procedures, please write them down and e-mail me - I'll post them here for others to reference.

Drive Construction Variables
If you have MS Excel, you can use my simplified spreadsheet to see how the variables interact.
Open it or download it here

There are a lot of variables that can be used. As a result, it is difficult to define exactly how your telescope should be built without some specifics. It helps to know that there is one constant: The telescope itself must follow the objects in the sky along the ecliptic at the rate of one revolution per day (RPD). Therefore, we must combine a number of variables together to turn the polar disc at the rate of 1 RPD. In this split ring design, there are six variables that directly affect RPD...
RPM = Revolutions Per Minute of Drive Motor
There are many different types of drive motors available. I use AC clock motors which turn at rates varying from a few revolutions per minute to revolutions per hour. I use AC motors because I can control the speed of the motor by changing the frequency of the power that runs it. Clock motor RPM ratings assume that it will be run on 60Hz AC power.
HZ = AC line frequency (Hertz)
Normal household AC has a frequency of 60 cycles per second (Hz). There are many simple circuits available that can convert DC power (such as a car battery) to AC power. During the conversion process, the frequency can be modified to be more or less than 60Hz and thus make the motor go a little faster or slower. This adjustment is very handy to adjust the speed of the telescope while observing or to make minor construction adjustments to compensate for other variables.
G1 = First Gear teeth (attached to motor)
I use worm gears because they don't transfer torque to the motor from the drive wheel. Worm gears are also the most efficient means of reducing motor speeds to the rate necessary to drive the telescope at 1RPD. However, I know that many other gear styles are available (such as helical gears), so I have included a way to use the number of teeth on two gears to factor in to the construction variable. If using worm gears, then use these gear factors for gear one: one turn worm use G1=1, two turn worm use G1=2, etc.
G2 = Second Gear teeth (attached to drive wheel)
The seond gear is directly attached to the drive wheel. This gear typically provides the most reduction in speed between the motor and the drive wheel. It is the ratio of this wheel's number of teeth to the number of teeth on the first gear that is important. You may be tempted to use plastic gears. I would advise against it because of the torque transfered from the drive wheel. This torque will easily wear the plastic down.
PD = Polar Disc diameter
The polar disc acts as a mount for the telescope tube assembly. Just as importantly, it is also a large bearing surface when interfaced with the drive wheel. The disc edge should be as round and true as possible, preferably with a durable surface that won't hold dirt or degrade. The polar disc aligns with the ecliptic plane (perpendicular to the polar axis) and turns at a rate of one clockwise revolution per day.
DW = Drive Wheel diameter
The drive wheel is the second surface of the large bearing formed with the polar disc. It turns in the opposite direction of the polar disc (counterclockwise). The drive wheel assembly also houses a slip clutch that provides the friction necessary to provide smooth tension for the rotation of the polar disc. I use a soft rubberized surface to counteract the hard edge of the polar disc. My favourite is polyurethane roller skate wheels. Roller skate bearings are also cheap and easy to use in this application.

So, use these variables to plug in to this formula and figure out what to build or buy.
(((((HZ/60)*RPM)*60)*(G1/G2))/(PD/DW))*24=RPD

Revolution Per Day (RPD) should be 1. A result of 0.x means RPD is too slow, while a result of 1.x is too fast.
Measurement units must be consistent. Use all inches or millimeters or centimeters, but don't mix.

Clear Skies!