Trig/Geometry help-Expansion Chamber

[newrider3]

Custom Expansion Chamber

So I'm doing some calculations to build an expansion chamber for a Yamaha DT175 using Gordon Jennings' formulas from the Two Stroke Tuner's Handbook, and I'm getting some figures that don't really make sense.

I'm trying to find the length of the cones, the formula he gives for this is ((D2-D1)/2)*cot(a); where D1 is the cone minor diameter, D2 is the major diameter, and a is 1/2 of the angle.

Given that my calculated head pipe ID is 1.63", and the desired diffuser cone outlet diameter is 4.07", with an 8 degree taper.
When I plug everything in, I end up with a length of only 1.5", which does not seem right. Plugging in the dimensions for the baffle cone (18 degrees, 4.07" inlet, 1.01" outlet) I calculate nearly 13", which does not seem right either (the baffle cone will always be much shorter than the diffuser).

Does anyone see the error in what I'm doing? Is there a better way to determine the length of a cone, given major diameter and angle?

 

[r97]

Unfortunately I can't find what is wrong. I tried it myself several times with cot and tan, no difference, getting numbers in the 1 to 1.5 range. What I did find though is that using this calculator I got about 17.45" for the diffuser and 9.66" for the baffle. Do those numbers sound more realistic? I'm going to go try some more things, hope that helps!

EDIT: Note that Google is giving me trigonometric ratios that are nothing like those from my calculator and math book. Google says Tan(4)=1.15782, my calc and math book say Tan(4)=0.06992.

EDIT2: Tried using the ratios from my calc, got the same answer as that online calc. Not sure what is up with google.

 

[newrider3]

That does sound much better, not sure why I didn't think of calculating just the triangle, I was just stuck on the cone idea. I'll play around with that a little later. Thanks!

Also, for future reference, Wolfram Alpha is far superior to Google when trying to do math stuff. This site saved my *** in Calculus.
http://www.wolframalpha.com/

 

[crazyman]

Alot of chamber formulas use millimeters. Is that the issue?

 

[newrider3]

Nope, this one calls for inches, as you would expect from a book written in America in the 1960's.

 

[newrider3]

Refined my angles and tuned length a little, then derped around on Solidworks and made a model of the chamber. Will start the build as soon as I get the money for some tubing and sheetmetal.

 

[r97]

Looks pretty good, can't wait to see how it works out!

 

[newrider3]

Finally found a cone calculator that works, so I got my patterns printed out and ready to transfer to steel. Also picked up a little silencer from my new favorite motorcycle junkyard that I plan to use with this pipe.

 

[matman55]

Sorry to get a little off topic but and correct me if im wrong but the purpose for a expansion chamber is to salvage fuel/air mixture that was pushed out the exhaust and re-burn what was not burned and it only works at a certain rpm range,Correct?

 

[newrider3]

Precisely. This chamber will be tuned to 'come on' at 7000 RPM, a little ways below the DT175 engine's redline. One thing that effects this rpm range is the angle of the baffle cone (rearmost cone, just before the stinger). A steep angle will prevent the engine from revving much higher than the tuned range, while a shallower angle (what I have chosen to use) will give you a broader usable RPM range.