The goals were to:
1) Get the formula (and values) enough to convert speed to RPM.
2) Identify the speeds in each gear where torque and power peaks.
3) Identify the potentially ideal efficiency points of rpm (and the req speeds to hold constant in each gear) of the engine.
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1) Firstly, below are the specific gear ratios for each gear:
1st: 3.454
2nd: 1.933
3rd: 1.315
4th: 1.095
5th. 0.933
Primary reduction ratio: 3.421
Final reduction ratio: 2.928
Here are the overall gear ratios for each gear (primary reduction ratio × specific gear ratio x final reduction ratio): -
1st: 34.597640352
2nd: 19.362257904
3rd: 13.17194472
4th: 10.96827336
5th: 9.345569904
* Speed in kmph should be converted to m/s by multiplying by (5/18), then multiply by 60 to get in units of m/min .
Now the rear tyre dimensions is given as 100/80-18 which means 18 inch rim diameter and for the remaining height it's 2 x (thickness of wheel heightwise).
Here it is 80% of the given 100 (as given by 2nd and 1st number in the notation) which is 80mm.
(Yes it's in milli metres and can vary based on air pressure and wear and tear, slightly changing equation)
=> Total diameter after conversions = 0.6172 metres.
Now we can use circumference in the formula.
Therefore,
RPM at given speed = (speed in kmph * (5/18) * 60 * total gear ratio for the given gear) / (pi*0.6172)
Peak RPM for torque: 6000 RPM
Peak RPM for power: 7500 RPM
2) By using above formula,
Speeds at each gear at which max torque is acheived sp125: -
1st: 20.177
2nd: 36.0515
3rd: 52.997
4th: 63.6453
5th: 74.6963
Speeds in each gear at which max power acheived at each gear sp125: -
1st: 25.221
2nd: 45.067
3rd: 66.2468
4th: 79.5567
5th: 93.37048
3) Caution: This section has data from real world experiments rather than calculations using purely formula due to the lack of relevant data. So the values are subject to change due to various factors like bike condition, winds, throttle sensitivity, road smoothness , weight load, etc.
Note: Also see the important "Edits" at the end of this post.
So in this case, there is a big flaw in the instantaneous mileage meter. It cant display above 99.99kmpl, which sounds ok but usually it's readings are much higher than actual mileage but it can be decently reliably used for relatively checking instantaneous mileage for our case.
3rd , 4th, 5th gears are out of the question since the peak values easily cross 99.99 so we can't find the peak value using this meter. First gear has so much torque, when I tried finding difference, the difference in fuel eff. readings between each rpm is so less that its arguably less than the error margin of this exp, so it's of barely any use.
Due to this, finally 2nd gear is the best to check as the instantaneous mileage reading at constant speed can't cross 99.99 kmpl.
Here is the summary of observations: -
* Only close to 20 kmph vaguely , the green eco indicator turned on after holding throttle constantly at each speed at 2nd gear.
* At 8 kmph 2nd gear (the lowest speed after leaving clutch fully but without giving any throttle) is actually NOT the most efficient rpm contrary to common opinions. It couldn't even touch 60 kmpl I think, mostly aroumd 55-60 kmpl at best.
* For a fun fact sake, I tried 3rd gear resting rpm at approx 12 kmph, it struggles, so it only reached like 68.4 - 71 kmpl or so in same as above point's conditions. (But this is not our goal, we need to find the ideal rpm in 2nd gear so in 5th gear we can cruise in the speed which we calculate later)
* In the rpms where I consistently easily got green eco indicator in 2nd gear were from very vaguely close to 20 kmph upto 26 kmph (constant speed for all trials). So it was clear compared to other speeds the best point lies around this region.
* Tried riding in extremely unrealistic constant speed in each of these speeds of this range in 2nd gear. Around 21 to 23 kmph showed good reading around 71kmpl approx (depends on how constant and how long you hold it).
Similarly for 21 kmph and below speeds , they were also quite economical but it was clear the efficiency point isn't below 21kmph 2nd gear, coz the rpm should be high enough for the engine to have enough torque for the load for maximum combustion efficiency. High rpms have high internal friction and poor valve timings wasting fuel so definitely not higher than the said range.
* Finally when I thought there isn't a single clear rpm point which exists, at around 25kmph 2nd gear I noticed in ALL my trials I got better readings relative to other speeds when relatively comparing readings in different trials. So I tried to see if it were a fluke or not.
* Tried on center stand to nullify road's effects : (these values are only from 1 trial)
66-68kmpl is usually coming for 23-24 kmph
Something around 21.5 kmph is coming around 72-74 kmpl
only at 25.5 kmph at 2nd gear it gives 80-82 kmpl mileage.
I can conclude that after several trials in real roads, around 26 kmph 2nd gear gave slightly higher inst. mileage and in extremely unrealistic constant speed touched 80+ kmpl (usually 74-77 kmpl) , the only speed which reached the mark without leaving the throttle to "artificially" temporarily increase the number.
But when I convert from 2nd to 5th gear, the error range can become bigger , so officially range is 25.5 to 26.99 kmph at 2nd gear .
Therefore, here is the final list of speeds at each gear to acheive peak efficiency rpm :- (Note: can vary by previously stated conditions, see edits at end of this post)
1st gear: (15 kmph) 14.2708453966 to 15.1047104806 kmph
2nd gear: (26 kmph) 25.5 to 26.99 kmph
3rd gear: (38 kmph) 37.4840304183 to 39.6742737643 kmph
4th gear: (46 kmph) 45.0150684932 to 47.6453607306 kmph
5th gear: (55 kmph) 52.8311897106 to 55.9181886388 kmph
Final ideal rpm range: 4243.93907423 to 4491.91825935 rpm
OR
Around 4410.36805753 rpm avg (26.5 kmph 2nd gear)
Around 73.5% of peak torque rpm.
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Edit: immediately after I gave 3rd service, the mileage numbers have slightly changed, but the 21 to 27 kmph at 2nd gear range is still better than other speeds, but the peak I said at 25...Well the mileage at that point isn't "peaking" higher than the others now😅
Will investigate further...
Edit 2: Finally, after 1 round of testing in centre stand, this time fresh after 3rd service engine oil, 26 kmph came as the topper. This is after engine is pretty heated too. So if you didn't understand Edit 1 properly, ill give context: Previously I said rpm ideal efficiency range comes when driving around 24.75 to 26 kmph in 2nd gear. But I'm getting slightly changed readings after new engine oil 3rd service (25.75 to 26.99 kmph at 2nd gear)
So do note it can be anywhere in these 2 ranges based on engine oil's age and how hot it is right now.
