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Quite a tricky gear ratio question to ponder

  1. Oct 17, 2011 #1
    If a 6 speed gear box has a 1st gear ratio of 7:1 and a sixth gear ratio of 1:1
    how would you calculate the 2nd,3rd,4th and 5th gear ratio's?

    If you use the equation for geometric progression which was my first thought - it doesn't work!

    Any ideas?
  2. jcsd
  3. Oct 17, 2011 #2


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    Welcome to PF, Crabbies.
    It can't be done in the way that you seem to want. There isn't usually any standard linear progression from one gear to the next. Each is chosen by the manufacturer for a specific reason.
    If you want an example that will really blow your mind, the A-833 in my Roadrunner is squirrelly. Pulling it into the 3rd gear gate actually puts it into 4th, which is 1:1. An upshift to the 4th gate drops it back into 3rd, which is a .73:1 overdrive. :rolleyes:
    Last edited: Oct 17, 2011
  4. Oct 17, 2011 #3
    ha that is odd!!

    My example wont be actually built it is the theory behind it that i was after. I need to find a way of calculating those values whether they are linear or not.
  5. Oct 17, 2011 #4


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    Ahhh... different matter entirely. I thought that you were trying to figure out the intermediates in an existing product.
    There are a few guys here who can give you much better advice than I can in regard to specifics. Generally, though, you want to achieve certain things in each range. I'm making what I think is a reasonable assumption in thinking of this as an internal-combustion vehicle application. I don't like to assume, but this is pretty much the only situation I'm aware of, other than lathes and other machine tools, wherein shiftable trannies are used.
    The goal in such devices is to keep the engine as close as possible to the middle of its power band regardless of vehicle speed. That is modified by what you want to achieve. Drag racing requires narrow-band shifting, whereas a highway cruiser is more open. Special situations such as tractor-trailer units have to combine aspects of both, but they're usually diesels and thus have a more restricted rpm range.
  6. Oct 17, 2011 #5


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    Why do you think that? My calculator says 1.00, 1.48, 2.18, 3.21, 4.74, 7.00.
  7. Oct 17, 2011 #6
    Most transmissions are 1:1 in 4th gear but some 6 speeds are 1:1 in 5th gear.
  8. Oct 18, 2011 #7
    Alpha zero I don't know how you achieved those figures? Which formula did you use?
  9. Oct 18, 2011 #8
    1) take out the tire.
    2) use a tachometer to measure the RPM at each speeds. u'll get N1, N2, N3, N4, N5, N6.
    3) use the relation: RPM at first speed/RPM at second speed= gear ratio of 2 to 1. i.e. N1/N2=T2/T1. =1/7
    4) the second gear ratio shd be N3/N2; the third shd be N4/N3 and so on.

    this will only work though if ur gear box has compound gear train.

    ur car has the sun and planet gear train or the epicyclic gear train. u need the structure to calculate the ratios. so u need to take it apart. I dont knw how it looks like but if u have a diagram post it, and then we can calculate.
  10. Oct 18, 2011 #9
    I don't have access to the gearbox as it is only a theoretical gearbox! There must be a way of using geometric progression. My friend has worked it out but won't tell me! Argghhh!

    The only clue he gave be is that the gears have a progressive increment of 1.4 but I need to know how he got to this?!?!
  11. Oct 18, 2011 #10
    for the record i think this question is incomplete. how can u have a gear train without knowing the type of gear train? and u need to atleast have one speed to get smthng good out of the problem to analyse (yes u can assume the speed but then where's the fun in tht). saying that i'll have a go at the answer.

    now,the clutch connects the engine shaft and the wheels at the 6th gear which makes the wheels run at the same speed as the engines [N2/N1=T2/T1=1] (pretty logical cause now u have the full power of the engine), and the speed shd decrease uniformly as u gear down from here. as the speed ratios are related to the gear ratios so they shd go down uniformly too. so the first gear ratio is 7:1 u need to divide it by 5 to equally distribute it amongst the 1-2, 2-3,3-4,4-5,5-6, gear ratios. (7/5=1.4). thts how ur friend got 1.4.
    but this is wrong cause it shd be 6/5=1.2 [7(first gear ratio)- 1(6th gear ratio)=6]. then u'll have the following gear ratios:
    2nd gear ratio: 5.8 ; 3rd gear ratio: 4.6; 4th gear ratio: 3.4; 5th gear ratio: 2.2. which is an AP with common difference of 1.2 rather than a GP.

    I hav no clue wat m talking abt:)
    Last edited: Oct 18, 2011
  12. Oct 25, 2011 #11
    1-2 = 19%
    2-3 = 18%
    3-4 = 17%
    4-5 = 13%
    5-6 = 8%

    Works very well on a dirt bike my friend uses.
  13. Oct 26, 2011 #12


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    You are very welcome here, and seem quite knowledgeable. That, unfortunately, is irrelevant when we have to break our brains in order to understand you. Please communicate in actual words. That "u" stuff, especially with no sense of capitalization or punctuation, just gives literate people headaches.
  14. Oct 26, 2011 #13
    Were you able to replicate AlephZero's result (geometric sequence)?
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