How long should my gnomon be?
The shortest shadow your gnomon will cast will be at solar noon on the summer solstice. The length of your gnomon is dependent on your latitude and the distance between the center of your dial and the numeral or indication that you require to be in shadow at solar noon.
No doubt you will wish all indications to lie in the shadow of the gnomon on every day of the year. The minimum length of the gnomon to meet this condition is shown by the relationship of the dial center at B to the symbol XII in the sketch below. Note that XII is closer to the dial center than the projection of the shadow on the summer solstice. i.e. The value for BC must be long enough to completely shade the numeral or indication.
A horizontal dial in the northern hemisphere
The required gnomon length BA can be found by experimenting with the angles in the sketch, or by a formula which solves the triangle ABC.
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The angle at A is: 90 - 23.45 = 66.55 The angle at B is the latitude of the dial The angle at C is: 180 - B - 66.55 Then by the law of sines: Side BA / sin C = BC / sin 66.55 Sin 66.5 = .91706 Thus: 
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In some cases the minimum condition may seem somewhat extreme, and your aesthetic sense may suggest that the gnomon should be longer for appearance sake. Don't be concerned, shadows are never wasted.
By Bob Terwilliger and Fer deVries