Gear Ratio Calculator

[BrettMavriK]

I am confused as to what exactly you plan to do,you mention a jack shaft presumably to get to the right side for the drive to the 3 speed hub,is that a direct drive from the jack shaft instead of via the crank ?,this means you won't be able to pedal the bike.If you intend to use the crank as intermediary you will need a freewheel crank.In that is the case there are 4 reduction stages internal engine / engine to jackshaft/ jackshaft to crankwheel/ crankwheel to hub input/.the calculator could still handle this if you combined the first 2 reductions (4 and 1.8) into one of 7.2 (you could put in say 72 and 10 ) then you have the last 2 reductions left in the calculator for the last 2 stages.
If you go directly from jackshaft to the hub,your ratio would be :based on your figures:
4x(18/10)x (20/28)=5.14,(assuming a 20t rear hub sprocket)This is far too small, you should have a reduction of around 13-17,which is about 3 times as large.So the input sprocket to the jackshaft has to be made larger and/or the output one smaller.For instance 20 t input and 10t output sprocket on the jackshaft gets you a 16:1 reduction.and about 19mph road speed at 5000 rpm.For a 20" wheel the following formula applies:
Speed= 0.06x rpm/R, R is overall reduction.For instance you would like 25mph at 6000 rpm,solve for R, R=6000x0.06/ 25=14.4 So you need around a 14:1 reduction.Understood?

It would be the latter set up you mentioned. The jack shaft will serve as an intermediary. It will have a fixed sprocket going to the rear wheel. Next to it, will be a freewheel sprocket going to the front crank. (yes, there are two crank shells on this chopper bike) (see photo)
I think the SA 3 Speed's freewheel is 19 I believe. So this leaves me with two sprocket gear choices; the left and right sprockets of the jackshaft.
Also the Sturmey Archer hub has 3 gears to think about:
75%,100%, and 133.3%

So 14:1 recommended for a 20" wheel, huh?
How about an 18t on the left and a 10t on the right?

Gears: 20-82-10-18-10-19 / Ratio: 14.02:1 / Speed: 25.5mph @ 6000rpm in 2nd gear (1:1)
(with 3rd gear left as an overdrive to push to the 30's)

'BrettMavriK

 

[wildemere]

try this spreadsheet

 

[wildemere]

An old English SA will be weak and quirky with its false neutral between 2nd and 3rd and it wants to spin its axle backwards under load..

And the fragile indicator chain and imperial threads it uses.

A new one from Taiwan might be better,

A Shimano model 3S is what I use, It is quite robust with the same ratios.

 

[BrettMavriK]

Pretty Cool Excel Spreadsheet.
Doesn't work for me though, considering I have two less sprockets and a 20" Tire. I did just plug in 19 for the three last slots to carry it through. It told me 29.1mph @ 6000 rpm with a 26" Tire, So I think I'm in the ball park with my two sprocket selections of 18 and 10 on the jack shaft.

(I am at 25.5mph in second gear/[1:1] @ 6000rpm) and I still have 3rd gear for 30+ mph.

The SA 3 Speed I am getting is Brand New, and especially made for the Stingray Chopper 4.25" (100mm) Rear Wheel. They are over in Taiwan now under Sun Race, after Raleigh died. They made them on a short run for the Stingray XL; adult sized chopper.

I'm not worried about the Sturmey in the Slightest....
'BrettMavriK

 

[duivendyk]

With your 12.66 ratio I come up with a speed of 28.4mph using my speed formula, this agrees closely with your 28.2mph.As best I remember the 3 speed SA hubs have ratios of 0.75-1- 1.33.Can you still get one ?.I would stay away from sprockets below 10t.Chain wear becomes a problem.10-17 and 10-19 ratios would get you:
4.1x1.7x1.9=13.3 reduction and a speed of 27 mph at 6k rpm, midrange on the hub with a min/max of 20/36 mph.Looks OK to me.
I would use the largest sprocket on the hub you can get and size the other ones appropriately.By the way there was nothing wrong with your calculations,trust me.

 

[BrettMavriK]

With your 12.66 ratio I come up with a speed of 28.4mph using my speed formula, this agrees closely with your 28.2mph.As best I remember the 3 speed SA hubs have ratios of 0.75-1- 1.33.Can you still get one ?.I would stay away from sprockets below 10t.Chain wear becomes a problem.10-17 and 10-19 ratios would get you:
4.1x1.7x1.9=13.3 reduction and a speed of 27 mph at 6k rpm, midrange on the hub with a min/max of 20/36 mph.Looks OK to me.
I would use the largest sprocket on the hub you can get and size the other ones appropriately.By the way there was nothing wrong with your calculations,trust me.

Now I have no idea what the normal accleration redline comfort zone is on these motors. Is 6000 a comfortable rpm for these HT motors to rev to when accelerating, or is 6000rpm's a comfortable cruising speed? Can you take them to 6500-7000 without rapping them out before shifting or should 6000 be the limit? If 6000 is normal cruise, then I think I like the 14:1 ratio better in cruising second gear / 1:1 @ 25mph. Then its' still in the power band for the beginning of 3rd above 6000rpm, say 6700 around 28mph before a 25% gear drop into 3rd to cruise in the mid 30's at 6000rpm. I also have to figure that this is a heavy steel chopper with a fat rear tire, and I am 185lbs.; so to be a little lower geared might prove the wiser.

With the reduction in the motor, the 10t gear off the crankcase, and the 19t gear on the rear wheel, I believe the 18t on the left input side of the jack shaft, and the 10t on the right output side, at 14:1 final ratio with the fat 20" tire, will be optimum with the weight of the bike and myself. I can always adjust, as this will be the starting point.

I really appreciate the help you guys.
This forum rocks.

'BrettMavriK

 

[duivendyk]

I make no claims about operating experience with the cheapy Chinese engines,they are not my cup of tea,but I would recommend that you take a good hard look at cautionary messages posted in these Forums,an initial partial rebuild may be in order,that could be some time&money well spent.These engines have a torque peak in the 5000-5500 rpm range and probably peak output around 6000-6500 rpm.Of course you can run them at higher speed but that is hard on the bearings (inertial forces!!)I would consider around4.5- 5k to be a good cruising speed.One factor that needs consideration is wether you live in the flats or wether there are substantial hills around (grades of 5% or more) because that affects your gearing strategy (towards lower gearing).If your gearing is too high,you are liable to run out of torque on hills then the engine gives up the ghost unless you can help out,but you have no pedals!.If you gear too low the thing turns into a buzz-saw at high speed.With your geared rear hub this is less of a problem,but steep hills require lower gearing.I would advise you to check if you can get different size hub input sprockets (they go I think, from 16 to 22t,that is over a 30% range!), take a middle one say 18 or19 ,then you can play around some with the overall ratios.These sprockets are not all that hard to change.

 

[BrettMavriK]

I make no claims about operating experience with the cheapy Chinese engines,they are not my cup of tea,but I would recommend that you take a good hard look at cautionary messages posted in these Forums,an initial partial rebuild may be in order,that could be some time&money well spent.These engines have a torque peak in the 5000-5500 rpm range and probably peak output around 6000-6500 rpm.I would consider around 5k to be a good cruising speed.One factor that needs consideration is wether you live in the flats or wether there are substantial hills around (grades of 5% or more) because that affects your gearing strategy (towards lower gearing).If your gearing is too high,you are liable to run out of torque on hills then the engine gives up the ghost unless you can help out,but you have no pedals!.If you gear too low the thing turns into a buzz-saw at high speed.With your geared rear hub this is less of a problem,but steep hills require lower gearing.I would advise you to check if you can get different size hub input sprockets (they go I think, from 16 to 22t,that is over a 30% range!), take a middle one say 18 or19 ,then you can play around some with the overall ratios.These sprockets are not all that hard to change.

Hmmmm......points well taken, definitely.
I live in FL (read: pancake land) flatter n' flat. But, I'm going to market this frame which DOES have pedals, by the way. The cranks are forward mounted on this chopper. I added a BMX bottom bracket shell to the seat post for the intermediate jack shaft. The jack shaft right side (output) has two sprockets; one for the rear wheel, one with a freewheel for the front crank. The pedals are not directly connected to the rear wheel, but way way of the intermediate jackshaft. The Sturmey Archer 3 Speed Hub I ordered has a 19t rear sprocket. I still think I'm gonna start with an 18t left and a 10t right on either side of the jackshaft at 14:1 and see what happens. My engine is a brand new 69cc with the roller bearings. I posted a photo of the latest mock up of my bike.

Here it is again,
'BrettMavriK

 

[duivendyk]

If it does no fase you unduly,as dedicated nerd&mathfreak I have come up with a sexy formula to compute how much power at the engine it takes to get up hills.If you are not a stranger to a calculator you can do some figuring it's not hard,all you got to do is plug innumbers and not make stupid mistakes,here goes:
P=0.36x(W/100)x(GR/100)xS, P is power in HP, W is total weight of bike+rider in lbs, GR is grade in % and S is speed in mph.Example W=350 lbs. Grade is 4 (4%) ,S=20.The answer tells us what power the engine has to produce to get 350 pounds up a 4% hill at 20 mph. We get P= 0.36x(350/100)x(4/100)x20
P=1.0 HP.That is the power the engine needs to deliver.I have assumed a drivetrain efficiency of 75% (that includes all the gearing between crankshaft& wheel tire.This may be optimistic with a geared hubs (gears are less efficient than chains)
Of course wether the engine is actually capable of delivering the power depends on the gearing.In midgear with a 14:1 reduction, 20mph requires 4800 rpm (0.06x4800/14=20.5),that looks OK.In low gear the rpm become 4800/0.75=6400 or at about top power capability.You can play around with the expression and solve for power or speed or change the steepness.I would not assume more than at the max 75% of advertised power to be available,considering the quality of these engines,overstressing them is probably not a wise thing to do.
One last thing, I have neglected the rolling&air resistance in this calculation in order not to overcomplicate things.Taking this into account I would guess the power requirement to be 25/35 % higher,depending on speed.(more at higher speed)

 

[BrettMavriK]

OK,
brain's starting to smoke again. I'm more of a right brained, creative individual. I like geomtery, but that's about as far as it goes unless I have to do some configuring. I've heard some different advice from many on just what the optimum gearing should be. I'm to the point where I'm going to order 3 pairs of gears for the jackshaft. 12,13,14:1 sets. Anyone make a tachometer for these little HT's????

'BrettMavriK
(I Liked Art Class Much Better)