Engineer Kelly
03-17-2008, 09:13 PM
This is a fun way to use the Law of Sines..Or Cosines to calculated the linear distance between fins. There are much easier ways of doing this..Like using a fin placement drawing. But i didnt realize there was one sitting on page 38 of "The Book" until i dug through my trig notes.
Anyway. It requires precise diameter measurements of the body tube you will be placing the fins on to be accurate.
2. Obtain a precise OD measurement of the body tube.
3. Decide how many fins you want to place on the body.
4. For first example lets choose 3 fins.
5. Divide 360 by 3 to give the center angle.
6. The fun begins! Draw a picture of your body diameter.
7. Create a triangle inside the circle with the center angle being 120 degrees and the other two angles being 30 and 30 of course.
8. That makes the hypotenuse (the longest side) equal to the distance between two fins.
9. Now to calculate that distance. The two short sides are both equal to each other and both are equal to the radius.
10. Using Law of Sines. Lets call the missing side a. Re-arrange equation to solve for a. Sub in 120 degrees for A, 30 degrees for B and 2 for b.
11. Solving for a gives us 3.464 (units of your choice) (The distance between the fins)
12. Then you can stretch a digital caliper across the body (to 3.464) and mark it where the fins are going to be located.
Refer to the picture below for visual explanation. The equation at the top is law of sines excluding sinC/c.
A=120
B=30
a=unknown
b=2
To get the second form of the equation multiply both sides by "a" then divide by SinB/b or multiply by its reciprocal.
The side opposite the angle being used is the lower case variable.
If using four fins the center angle will be 90 degrees making it a lot easier and you can just use the pythag. theorem or use the right triangle definitions of Sin Cos and Tan.
What other ways are there?
I typed this up really fast. Ill make an updated version if anyone is interested in it.
http://img80.imageshack.us/img80/9852/0317082056mu5.jpg
Anyway. It requires precise diameter measurements of the body tube you will be placing the fins on to be accurate.
2. Obtain a precise OD measurement of the body tube.
3. Decide how many fins you want to place on the body.
4. For first example lets choose 3 fins.
5. Divide 360 by 3 to give the center angle.
6. The fun begins! Draw a picture of your body diameter.
7. Create a triangle inside the circle with the center angle being 120 degrees and the other two angles being 30 and 30 of course.
8. That makes the hypotenuse (the longest side) equal to the distance between two fins.
9. Now to calculate that distance. The two short sides are both equal to each other and both are equal to the radius.
10. Using Law of Sines. Lets call the missing side a. Re-arrange equation to solve for a. Sub in 120 degrees for A, 30 degrees for B and 2 for b.
11. Solving for a gives us 3.464 (units of your choice) (The distance between the fins)
12. Then you can stretch a digital caliper across the body (to 3.464) and mark it where the fins are going to be located.
Refer to the picture below for visual explanation. The equation at the top is law of sines excluding sinC/c.
A=120
B=30
a=unknown
b=2
To get the second form of the equation multiply both sides by "a" then divide by SinB/b or multiply by its reciprocal.
The side opposite the angle being used is the lower case variable.
If using four fins the center angle will be 90 degrees making it a lot easier and you can just use the pythag. theorem or use the right triangle definitions of Sin Cos and Tan.
What other ways are there?
I typed this up really fast. Ill make an updated version if anyone is interested in it.
http://img80.imageshack.us/img80/9852/0317082056mu5.jpg