Let's see if I can fix this sundial - rectifying stupid...

[WobblyHand]

So for a horizontal sundial, the angle from noon for each hour is given by H = arctan( sin(L) tan( 15deg * t)). (From the previous Wikipedia link.) where L is the latitude angle (42.8 in my case) and t is in hours relative to noon. So lets see what angles I get. Lets just do 1-8 pm

1pm. 10.32
2pm. 21.42
3pm. 34.19
4pm. 49.64
5pm. 68.48
6pm. 90.00
7pm -68.48
8pm. -49.64

Since sin and tan are odd functions, then the earlier hours are negative of the sequence (relative to noon)

4am = 49.64
5am = 68.48
6am = -90.00
7am = -68.48
8am = -49.64
9am = -34.19
10am = -21.42
11am = -10.32

Well, shoot, now I have to go get the sundial and measure/estimate what is there... I wonder how far off it is. You can clearly see it depends on the latitude. Since I just wrote a dumb program to calculate this for me, lets see what happens if the gnomon angle is 54.5 degrees. (What I have right now, which is incorrect for my latitude)

1pm. 12.31
2pm. 25.17
3pm. 39.15
4pm. 54.66
5pm. 71.78
6pm. 90.00
7pm -71.78
8pm. -54.66

It's off by up to 5 degrees in some areas, but the error varies with the hour. Sorry, geeking out on this. Never appreciated this stuff on sundials. So the scale isn't linear and neither is the error. I wonder what the dial I have measures to?

latitude
time. 42.8. 54.5. difference

1pm. 10.32 12.31 1.98 deg
2pm. 21.42 25.17 3.76
3pm. 34.19 39.15 4.96
4pm 49.64 54.65 5.01
5pm 68.48. 71.78 3.30
6pm 90.00 90.00 0
7pm -68.48 -71.78 -3.30
8pm -49.64 -54.65 -5.01

 

[WobblyHand]

I was referring to the shop clerk telling @CJ5Dave that it doesn't spin. the clerk probably thinks that the dial needs to rotate.

Yeah, that's sad. I don't know of any sundials that spin.

 

[CJ5Dave]

I think these were used when precise time was not a big deal.

 

[WobblyHand]

I think these were used when precise time was not a big deal.

Definitely. But a custom one could be reasonably accurate for it's location. Would be neat to be able to cnc one.

Hmm, I'm going to prototype one and print it. It will be in two pieces. Guess I better learn how to extrude the Roman numerals. If it works, maybe I'll get it cast. First I'll make a small one.