Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
techtalk:ref:svcproc11k [2023/10/29 00:59] hippysmack [Formulas] |
techtalk:ref:svcproc11k [2024/01/21 21:01] (current) hippysmack |
||
|---|---|---|---|
| Line 26: | Line 26: | ||
| {{:techtalk:ref:svcproc:gear_ratio_and_internal_torque_ratio_chart_by_hippysmack.png?direct&450|}} {{:techtalk:ref:svcproc:gear_ratio_and_overall_torque_ratio_chart_by_hippysmack.png?direct&450|}} \\ | {{:techtalk:ref:svcproc:gear_ratio_and_internal_torque_ratio_chart_by_hippysmack.png?direct&450|}} {{:techtalk:ref:svcproc:gear_ratio_and_overall_torque_ratio_chart_by_hippysmack.png?direct&450|}} \\ | ||
| + | |||
| + | The internal gear ratio chart shows the rate of how the transmission gears reduce speed and increase torque to the transmission sprocket (accept 5th GEAR). \\ | ||
| + | Changes to the internal ratios (1st-4th GEAR) affect final drive ratios and thus rear wheel torque and speed. \\ | ||
| + | |||
| + | The overall gear ratio chart shows the rate of how the (combined) ratios change engine sprocket torque and speed to the rear wheel. A lower gear provides a greater torque multiplication (drive ratio) between the engine and the rear wheel. Our motorcycles accelerate harder, the lower the gear they are in. Downshifting to a lower gear has the effect of increasing drive ratio and thus increasing the torque multiplication between the engine and the rear wheel. ((AC2W of the XLFORUM https://www.xlforum.net/forum/sportster-buell-motorcycle-racing/sportster-motorcycle-drag-racing/36229-when-to-shift-peak-hp-or-tq/page3?t=70371&page=3)) \\ | ||
| + | |||
| + | The values are ONLY ratios. They do not show how much torque is produced. They do show at what (rate) torque is multiplied through the different gear teeth changes. \\ | ||
| + | More rpm equals more torque in any transmission GEAR and given at the (rate) shown. \\ | ||
| ====== General Terminology ====== | ====== General Terminology ====== | ||
| Line 51: | Line 59: | ||
| {{:techtalk:ref:svcproc:gear_ratio_-_driver_and_driven_gears_in_neutral_by_hippysmack.png?direct&450|}} {{:techtalk:ref:svcproc:gear_ratio_-_driver_and_driven_gears_in_1st_by_hippysmack.png?direct&450|}} \\ | {{:techtalk:ref:svcproc:gear_ratio_-_driver_and_driven_gears_in_neutral_by_hippysmack.png?direct&450|}} {{:techtalk:ref:svcproc:gear_ratio_-_driver_and_driven_gears_in_1st_by_hippysmack.png?direct&450|}} \\ | ||
| - | ===== Torque vs Speed ===== | + | ===== Torque vs Speed (ratios) ===== |
| - | The gear ratio shows the trade-off between torque and speed. Speed is RPM and Torque is PUSH. ((https://motorcycleinfo.calsci.com/Horsepower.html)) RPM is what is needed on the highway and Torque is the ability to move the bike faster from a stand still. Progressively through the upper gear changes, torque is lowered and speed is gained through gear ratio changes. As with the 2 gear train mentioned above; \\ | + | The gear ratio shows the trade-off between torque and speed. Speed is RPM and Torque is PUSH. ((https://motorcycleinfo.calsci.com/Horsepower.html)) RPM is what is needed on the highway and Torque is the ability to move the bike faster from a stand still. Progressively through the upper gear changes, torque is lowered and speed is gained through gear ratio changes. As with the 2 gear train mentioned below; \\ |
| If the driving gear is smaller than the driven gear, the result is the driven gear turns slower (less speed) but with (more torque) applied downstream of it. \\ | If the driving gear is smaller than the driven gear, the result is the driven gear turns slower (less speed) but with (more torque) applied downstream of it. \\ | ||
| If the driving gear is larger than the driven gear, the result is the driven gear turns faster (more speed) but with (less torque) downstream of it. \\ | If the driving gear is larger than the driven gear, the result is the driven gear turns faster (more speed) but with (less torque) downstream of it. \\ | ||
| Example: A 20 teeth gear is driving a 40 teeth gear. The input speed is 1000 RPM and the input torque is 50 ft/lbs. \\ | Example: A 20 teeth gear is driving a 40 teeth gear. The input speed is 1000 RPM and the input torque is 50 ft/lbs. \\ | ||
| Using the gear ratio (20/40 = 0.5:1), the output speed was reduced to 500 RPM (1000 x 0.5 = 500). \\ | Using the gear ratio (20/40 = 0.5:1), the output speed was reduced to 500 RPM (1000 x 0.5 = 500). \\ | ||
| - | Using the inverse gear ratio, (40/20 = 2:1) then multiplying the known input torque (50 ft/lbs) by the result, (50 x 2 = 100 ft/lbs). \\ | + | Using the inverse gear ratio, (40/20 = 2:1) then multiplying the example input torque (50 ft/lbs) by the result, (50 x 2 = 100 ft/lbs). \\ |
| So the output speed was cut in half by this gearset but the output torque doubled (this does not take into account efficiency loss). | So the output speed was cut in half by this gearset but the output torque doubled (this does not take into account efficiency loss). | ||
| However adding gear efficiency, ex. 99% for a spur gears, the formula changes to (40/20) x 50 x .99 = 99 ft/lbs of output torque. | However adding gear efficiency, ex. 99% for a spur gears, the formula changes to (40/20) x 50 x .99 = 99 ft/lbs of output torque. | ||
| The same mathing applies if the driver gear has more teeth than the driven gear. The results are just in reverse. \\ | The same mathing applies if the driver gear has more teeth than the driven gear. The results are just in reverse. \\ | ||
| - | {{:techtalk:ref:svcproc:gear_ratio_and_torque.png?direct&400|}} ((drawing by Hippysmack)) \\ | + | {{:techtalk:ref:svcproc:gear_ratio_and_torque_by_hippysmack.png?direct&400|}} ((drawing by Hippysmack)) \\ |
| + | |||
| + | ===== Torque vs Speed (horsepower) ===== | ||
| + | Below is a compilation of quotes from aswracing of the XLFORUM; \\ | ||
| + | |||
| + | Torque essentially comes from two things: cylinder pressure and the mechanical advantage it has on the crank. ((aswracing of the XLFORUM https://www.xlforum.net/forum/sportster-buell-motorcycle-racing/sportster-motorcycle-drag-racing/36229-when-to-shift-peak-hp-or-tq/page3?t=70371&page=3)) Mechanical advantage on the crank comes from both the bore and the stroke. This is easy to visualize when you think of the stroke as a function of how far the crankpin is from the center of the crank. The stroke is essentially the size of the lever. More stroke means the rod has more leverage to turn the crank. But bore size also gives more leverage. Pressure is described in pounds per square inch. Well, with a bigger bore, you've got more square inches to push on. So the bottom line is that both the bore and the stroke contribute to the torque. \\ | ||
| + | |||
| + | The other ingredient of torque is the pressure you build. ((aswracing of the XLFORUM https://www.xlforum.net/forum/sportster-buell-motorcycle-racing/sportster-motorcycle-drag-racing/36229-when-to-shift-peak-hp-or-tq/page3?t=70371&page=3)) That pressure is a function of a whole bunch of things, including things like how well you filled the cylinder and how hard you compressed it on the compression stroke. The piston moving out of the way regulates the pressure. Ever wonder why a motor pings at high load? It's harder to move the piston out of the way at high load, hence the pressure gets too high. So cylinder pressure has a close relationship to the torque. Horsepower is and always will be torque times rpm (divided by 5252, but conceptually, you can ignore that part, all it really does is scale the number to what Watt's horse could do). | ||
| + | |||
| + | Downshifting to a lower gear has the effect of increasing drive ratio and thus increasing the torque multiplication between engine and rear wheel. ((AC2W of the XLFORUM https://www.xlforum.net/forum/sportster-buell-motorcycle-racing/sportster-motorcycle-drag-racing/36229-when-to-shift-peak-hp-or-tq/page3?t=70371&page=3)) However, not everyone understands that. | ||
| + | Some people latch on to this notion that "torque accelerates the bike" and argue emotionally around that. ((aswracing of the XLFORUM https://www.xlforum.net/forum/sportster-buell-motorcycle-racing/sportster-motorcycle-drag-racing/36229-when-to-shift-peak-hp-or-tq/page3?t=70371&page=3)) What they fail to understand is that torque at the rear wheel is what accelerates the bike, not torque at the engine. And the torque shown on a dyno sheet is torque at the engine, i.e. upstream from the gearing. But that gear reduction in the primary, transmission, and secondary changes everything. It can take less torque and make it more. The more rpm you have, the more gear reduction you can apply for a given rear wheel speed. So engine rpm ends up being every bit as important as engine torque when it comes to accelerating the bike. Hence when we talk performance, we don't talk in terms of torque, nor do we talk in terms of rpm, we talk in terms of their combination. What matters is the total combination of torque and rpm you can make, which is better known as "horsepower". \\ | ||
| + | |||
| + | The torque peak means absolutely nothing for maximum acceleration. ((aswracing of the XLFORUM https://www.xlforum.net/forum/sportster-buell-motorcycle-racing/sportster-motorcycle-drag-racing/36229-when-to-shift-peak-hp-or-tq?t=70371)) \\ | ||
| + | Get two identical bikes going side by side, with both at the engine's torque peak. ((aswracing of the XLFORUM https://www.xlforum.net/forum/sportster-buell-motorcycle-racing/sportster-motorcycle-drag-racing/36229-when-to-shift-peak-hp-or-tq?t=70371)) Whack one of them wide open. At the same time, downshift the other bike to put the motor at the power peak instead and whack it wide open. It won't even be close. The bike at it's power peak will run away from the other bike. Why? Because when you downshift, you multiply the torque. That means that even though the motor is making less torque, since you have more gear reduction in the lower gear, you end up with more torque at the rear wheel, and that's what accelerates the bike. \\ | ||
| + | |||
| + | This is exactly what a horsepower curve (on a dyno chart) is all about. It takes into account that the rpm the motor is turning is also a component of the performance. The more rpm you're turning, the more gear reduction you can apply at a given speed, and hence the more you can multiply the motor's torque. Horsepower is a complete description of performance, torque is not. At any given speed, maximum torque at the rear wheel occurs at the power peak, not the torque peak. \\ | ||
| + | |||
| + | Torque is twisting force, without any regard for speed. But speed is enormously important. For example, if you have 80 ft-lbs at 3000 rpm, you can get twice as much done as if you had 80 ft-lbs at 1500 rpm. You're making the same torque, but you're making it twice as fast. In fact, you could take that 80 ft-lbs at 3000 rpm, gear it down 2:1, and have 160ft-lbs at 1500 rpm. In other words, you have the option of making twice the torque, but doing it at the same speed as the weaker motor. So you see, having more rpm is a huge advantage. You can make small torque into big torque if you have more rpm. That's what gear reduction is all about. It's also exactly why a 600 race rep with 40 ft-lbs at 15,000 rpm will beat up on a Sportster making 80 ft-lbs at 5000 rpm. It may only have half the torque, but it's turning three times the rpm. So for any given rear wheel speed, it can have three times the gear reduction through the primary & tranny & final drive, which multiplies it's torque three additional times over that of the Sportster. Hence more torque reaches the rear wheel at any given rear wheel speed. Three times 40 is 120, and that's more than the 80 that the Sportster has. That's exactly why you talk horsepower when you're talking about performance. Horsepower is literally torque times rpm. It combines the twisting force (torque) with the speed of twisting (rpm). Both are equally important when you're talking about performance. They're also totally interchangeable. Gear something down, you decrease rpm and increase torque. Gear something up, you increase rpm and decrease torque. \\ | ||
| + | |||
| + | Here's a motor we built for a guy several years ago. \\ | ||
| + | The torque peak is 109.4 ft-lbs at 4600 rpm. The power peak is 117.6 hp at 6700 rpm. Pick a rear wheel speed. Let's just say 500rpm. If we have the motor at 4600rpm, and we're in a gear, that gives us 500rpm rear wheel speed, that means we have 9.2 of overall gear reduction (4600 divided by 500 is 9.2). Well, if the motor is making 109.4 ft-lbs, and you've got 9.2 of gear reduction between the crank and the rear wheel, you've got 109.4 times 9.2 equals 1006.48 ft-lbs of torque at the rear wheel. Okay, now let's see what happens at the power peak instead. If we have the bike at 6700rpm, and it's got 117.6 horsepower, that means it's making 92.2 ft-lbs of torque (torque = (hp times 5252) divided by rpm). If you work that out, you'll get 92.2 ft-lbs, and you can see on the chart that's about right. \\ | ||
| + | If we have the motor at 6700rpm, and we're in a gear that gives us 500rpm rear wheel speed, that means we have 13.4 of overall gear reduction (6700 divided by 500 is 13.4). Well, if the motor is making 92.2 ft-lbs, and you've got 13.4 of gear reduction between the crank an the rear wheel, you've got (92.2 times 13.4 equals 1235.48 ft-lbs) of torque at the rear wheel. 1235.48 is more than 1006.48. The power peak wins. \\ | ||
| + | So as you can see, at the same rear wheel speed, you put more torque to the rear wheel when the motor is at the horsepower peak, not when the motor is at the torque peak. This is exactly why horsepower is the meaningful number. It takes the engine's rpm into consideration. The engine's rpm is every bit as important as the engine's torque, because the more engine rpm we have, the more gear reduction we can apply for a given rear wheel speed. And the more gear reduction we can apply, the more we multiply the engine's torque. There's a much more direct way to do that calculation, I did it the long way just to illustrate the concept. But the short way is just to calculate rear wheel torque directly, knowing rear wheel rpm and rear wheel horsepower. Remember, any time you know any two of the three components (torque, rpm, or power), you can calculate the third. \\ | ||
| ====== Formulas ====== | ====== Formulas ====== | ||
| Line 73: | Line 103: | ||
| * **Output Torque ratio** for 4 gears = (number of teeth on driven gear x number of teeth on driven gear) / (number of teeth on driving gear x number of teeth on driving gear) | * **Output Torque ratio** for 4 gears = (number of teeth on driven gear x number of teeth on driven gear) / (number of teeth on driving gear x number of teeth on driving gear) | ||
| * **Output Torque** = (input torque) x (output torque ratio) | * **Output Torque** = (input torque) x (output torque ratio) | ||
| + | * **Power[hp]** = torque[lb-ft] x RPM ÷ 5252 | ||
| ====== Examples of Gear Ratio Calculations ====== | ====== Examples of Gear Ratio Calculations ====== | ||
| Line 97: | Line 128: | ||
| ===== Internal Gear Ratio (4 gears) ===== | ===== Internal Gear Ratio (4 gears) ===== | ||
| - | Internal ratios are calculated per transmission GEAR selected. There are a total of 5 ratios that make up the internal ratio (1st-5th transmission GEAR). \\ | + | Internal ratios are calculated per each transmission GEAR selected. \\ |
| - | However, Sportster transmissions have a 1:1 ratio in 5th gear so it doesn't need calculating further. \\ | + | There are a total of 5 ratios that make up the internal ratio (1st-5th transmission GEAR) and they are calculated individually. \\ |
| + | However, Sportster transmissions have an internal ratio of 1:1 in 5th gear so it doesn't need calculating further. \\ | ||
| [[techtalk:evo:transfinal01|Click Here]] to see the gearing chart in the Evo section "Primary/Transmission/Final Gear Ratios". The internal ratios are listed for 1986 and up Sportsters. \\ | [[techtalk:evo:transfinal01|Click Here]] to see the gearing chart in the Evo section "Primary/Transmission/Final Gear Ratios". The internal ratios are listed for 1986 and up Sportsters. \\ | ||
| Line 113: | Line 145: | ||
| The example illustration below shows the gears colored red in the Power Flow for 2nd gear. \\ | The example illustration below shows the gears colored red in the Power Flow for 2nd gear. \\ | ||
| **Note**, C3 is in red only because it takes C3 gear dogs to lock C2 gear to the countershaft. \\ | **Note**, C3 is in red only because it takes C3 gear dogs to lock C2 gear to the countershaft. \\ | ||
| - | |||
| This example uses the stock gears from a 1998 XL1200; M2 (29T) - C2 (34T) gearset and C5 (25T) - M5 (42T) gearset. \\ | This example uses the stock gears from a 1998 XL1200; M2 (29T) - C2 (34T) gearset and C5 (25T) - M5 (42T) gearset. \\ | ||
| Line 155: | Line 186: | ||
| * Plug the numbers from the example above in the new formula: 0.99 x (1,428 / 725) = 1.949958620689655 (or 1.950:1) | * Plug the numbers from the example above in the new formula: 0.99 x (1,428 / 725) = 1.949958620689655 (or 1.950:1) | ||
| * So the actual internal ratio in that instance would be slightly lower than the advertised ratios. | * So the actual internal ratio in that instance would be slightly lower than the advertised ratios. | ||
| + | |||
| + | **Here is why transmission 5th GEAR Internal Ratio is 1:1**. \\ | ||
| + | Any gear that is splined to or locked to a shaft rotates at the same speed the shaft rotates. \\ | ||
| + | Example: In 5th GEAR, if the clutch sprocket is rotating the mainshaft at 1000 RPM, all gears attached to it also rotate at 1000 RPM. \\ (includes M1 and M2 since they are splined to the mainshaft and M5 since M2 dogs lock M5 to the mainshaft). \\ | ||
| + | M5 is splined to the transmission sprocket and these two gears always rotate at the same speed. \\ | ||
| + | So each of these gears rotate at the same speed. \\ | ||
| + | (clutch sprocket RPM / M5 RPM) = 1000 / 1000 or 1, (expressed as 1:1). | ||
| + | |||
| + | {{:techtalk:ref:susp:gear_ratio_and_internal_ratio_5th_by_hippysmack.png?direct&400|}} ((drawing by Hippysmack)) \\ | ||
| ===== Primary Drive Ratio ===== | ===== Primary Drive Ratio ===== | ||
| Line 252: | Line 292: | ||
| |:::|9.04:1|6.62:1|4.82:1|3.97:1|3.36:1| | |:::|9.04:1|6.62:1|4.82:1|3.97:1|3.36:1| | ||
| + | The above chart shows ADVERTISED RATIOS ONLY (often referred to as Ideal ratios). \\ | ||
| + | The ACTUAL RATIOS WILL BE LOWER (due to efficiency loss). \\ | ||
| + | To quote KHK Gears: \\ | ||
| + | The efficiency shown above is the transmission efficiency of gears without regard to the loss in bearings or agitation of grease. ((https://khkgears.net/new/gear_knowledge/the-first-step-of-mechanism-design-using-gears/know-about-gear-transmission-torque.html)) \\ | ||
| + | You cannot calculate a gear's transmission torque simply as shown above because of the following reasons: \\ | ||
| + | * Heat is produced by meshing teeth and energy is lost. \\ | ||
| + | * Hammering sound is produced by meshing teeth and energy is lost. \\ | ||
| + | Therefore, the torque (turning force) is reduced by as much as the energy is lost. \\ | ||
| + | The ratio of input to output forces of gears is called “machine efficiency” and its approximate value is known according to the gear type. \\ | ||
