Math for shorter throw in a shifter

Let's say I'm looking to reduce throw by about 50%.  Doing so by lenghting the distance under the pivot point.  This should change the total angle I'm moving the shifter at the top.  I scratched out some math to try to see how much I would need to add.  Pretty sure im on the right track.  Looks like it would take adding 2.5" to it.  Seems like alot.  So I'm not quite sure this works the way I'm thinking.  

Math in pics

A reduced throw  is often a combination of a shorter lever with a raised fulcrum point  as in your diagram. If you feel that even with the change in ratio, the lever may be on the long side, combining the shorter lever will make it even faster.

For instance this one for the AR5 trans reduces action at the knob from 4" to 2.6"  http://www.ddmworks.com/DDMWorks-Short-Throw-Shifter_p_484.html

If you want to reduce the throw by half, the easy math is to raise the pivot by double the height.  If your current pivot is 2" above the end of the shift stub, you need to raise the pivot by another 2"

50% reduction is a lot.  Many aftermarket shifters reduce throw by 10-30%.  Not doubting you, just posing a thought bubble.

Your math looks on par, but part of the reduction in throw comes from having the same overall length of the whole shifter.  Yours is 2.5" taller at the knob.  If you re-do the math with 6.5" above the pivot (to keep the same overall height) you'll find you've reduced the throw by a significant difference, maybe more than 50%.

Curtis73 said:

If you want to reduce the throw by half, the easy math is to raise the pivot by double the height.  If your current pivot is 2" above the end of the shift stub, you need to raise the pivot by another 2"

50% reduction is a lot.  Many aftermarket shifters reduce throw by 10-30%.  Not doubting you, just posing a thought bubble.

Just to elaborate, unless you have a shifter with a particularly long throw (~5" doesn't sound terrible) or a particularly fast shifting transmission, that much of a reduction may well not actually speed up shifts any, at least not without being hard on the synchros. Also keep in mind that depending on how the linkage works you may be shortening the side to side throw as well (ie 1 and 3 are closer together), too much of that and it'll get hard to find the right gear.

I've lengthened the bottom of some FWD shifters, and chose the length based on whatever was going to get in the way (namely exhaust).

Did some more quick maths.

If you keep the same overall height (in your case, 11 inches) and move the pivot, you don't need to go double the distance to get half the throw.  Check out my math here.  You have to make right triangles, and in truth this assumes linear travel (which we know it travels in an arc... but I'm not dragging out my trig and calculus for you fools)  

Moving the pivot up to 4" thereby leaving 7" of stick, you do it this way.  Find half the 1.75" throw which is 7/8" or .875".  Find the angle which is done sin(x) = .875/4.  or inverse sin of .875/4.  This gets you 16.95 degrees.  Now work backwards for the top.  sin(16.95) = x/7  That gets you 1.53 inches which you double to get the total throw of 3.06" which is about a 33% reduction.

Do the same again, but use 4.5" below the pivot and 6.5" above.  You get 2.52" throw, which is about a 45% reduction.

You can figure it out by starting with an actual 50% reduction (2.3") but you have to pick an actual pivot distance for this to work.  If you're looking at keeping the same overall height of the knob, its a bit quicker to do trial and error like this.  If you want to pick a different stick height, you can flip these equations around and find an actual pivot height.

If my maths is correct, going 1.5 times taller from the shift rail to the pivot nets about 45% reduction in throw... far less than the double distance needed if you keep the 8" above the pivot.

In reply to Curtis73 :

Yep I've actually preferred on my Nissan to raise the pivot on the stock arm. Luckily it's merely a press fit delrin ball inside a cage so just pop the shifter out and clamp the ball in a padded vise and give it a few whacks with your trusty ol thumb detector. 

In reply to ChrisLS8 :

Mine seems to be press in, but I went after it with a BFH in a vise and couldn't get it move.