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====== PlayGround ======
====== Calculating Gear Ratios ======
====== General Information ======
**If you are researching how to calculate gear ratios, it can be confusing since there are several ways to come to the same answer**. And once there were general practices that have gotten skewed by the years since. But math doesn't change, only the way you look at it does. Simple math is all that is needed to find the different ratios and information about the gear train. Simple formulas are used to achieve this. The trouble can be which formula to use for what purpose. \\

**If there was only one gear on a shaft, there'd be no need to find a ratio**. You know how many turns are made based off the RPM of the gear shaft. When you add a second gear and shaft with gear teeth meshed to the first and both are different sizes, one will turn at a different speed than the other. Therefore, their respective shafts will also turn at different speeds. \\

**However, it is Harley Davidson that spurs the initial confusion**. \\ The manuals state verbiage like "Internal gear ratios indicate number of mainshaft revolutions required to drive output sprocket one revolution." This verbiage refers to speed (or RPM). And the service manual lists the different internal ratio values for (i.e. for 883 and 1200) engines. If you instead run the numbers yourself, you'll find the GEAR RATIO does not match the specs they list in the manuals. The gear ratio formula represents a change in speed due to the different number of teeth on the driven gear as opposed to the driver gear. So you divide the driver gear teeth BY the driven gear teeth and you find how much faster or slower the driven gear turns as opposed to the driver gear. \\

**Driver vs Driven Gear** \\
Determining which is which is crucial in calculating the gear ratio. \\
When the teeth are meshed together on the 2 separate shafts, one gear drives the other. The gear making the other move is called the driver gear and the other gear is being driven (thus driven gear). The driver gear is closest the power source. The power source is the engine by way of the engine sprocket (driver) which drives the mainshaft by way of the clutch sprocket (driven).  The mainshaft receives power from the engine by way of the clutch. The clutch is between the engine and mainshaft and acts more like an on/off switch. With the clutch engaged, the mainshaft receives power from the engine. With the clutch dis-engaged, the mainshaft does not receive power from the engine. The mainshaft drives the countershaft in 1st-4th GEAR and the countershaft drives the M% and thus the transmission sprocket. And in 5th GEAR, the mainshaft drives M5 and thus the transmission sprocket, taking the countershaft out of the power flow. \\

In the (left) drawing below, there are only 2 gears that are splined to the transmission mainshaft (M1 and M2 gears). The other 3 gears on the mainshaft are sleeved over bearings on the shaft and have to be locked to the mainshaft by way of either M1 or M3 in order to turn the shaft. There are '+' signs above/below each gear in RED or BLACK. Such as M4 has a BLACK '+' and C4 has a RED '+' and M1 has a RED '+'. The BLACK '+' gears are SLEEVED over the shaft on which they are located. This means they can turn separately from the shaft unless otherwise engaged. The RED '+' gears are SPLINED to the shaft on which they are located. This means they always turn whenever that shaft turns. Both M1 and M3 are sliding gears (as is C3) and they are moved by way of the shift forks when you move the shifter pedal. \\ M1 and M2 (in Neutral) are the driving gears and they are both driving their respective counter gears (C1 and C2). Neither C1 nor C2 are splined to the countershaft, they just sit there and spin while the transmission is in Neutral. So power stops there and allows the bike to idle without being "in GEAR" \\

In the (right) drawing below, M1 and M2 are still moving and turning their respective gears but now the power from the engine is being used to turn the engine sprocket (to rear tire) so the emphasis is on that flow of power. M1 is (driving) and C1 is being (driven). C1, being sleeved on the shaft, is locked to the countershaft by C3 which makes the countershaft turn. Following the flow of power,C5 is splined to the countershaft and turns when the shaft turns. However, the mainshaft 5th gear (M5) is sleeved and can't turn on it's own. With C5's teeth in constant mesh with M5, C5 is (driving) and M5 is being (driven). \\ M5 is splined to the transmission sprocket which turns when M5 turns. The transmission sprocket drives the rear wheel sprocket. \\
 
{{:techtalk:ref:svcproc:1991-2003_trans-flow-0-neutral_by_hippysmack.png?direct&400|}} {{:techtalk:ref:svcproc:1991-2003_trans-flow-1st_by_hippysmack.png?direct&400|}} ((drawing by Hippysmack)) \\
\\
**The standard gear ratio tells you how fast the second gear (driven gear) turns as opposed to how fast the first gear (driver gear) turns.** \\
So you know how fast the first one is turning but now need a ratio of the two gears to find out how fast (or slow) the **second gear** is turning. __Normally, to find the gear ratio, you'll divide the teeth count of the first gear (driver gear) by the teeth count of the second gear (driven gear)__. Example:  A 20 teeth gear is driving a 40 teeth gear. By dividing the first gear teeth by the second gear teeth, you get a number of 0.5 (20 / 40 = 0.5). That means the second gear will only turn at a rate of 0.5 (or 1/2) turns when the first gear has made 1 full turn on it's shaft. And if the RPM of the first gear is turning at 1000 RPM, the second gear is turning at 500 RPM (1000 x 0.5 = 500). \\

**The inverse of the gear ratio tells you how fast the first gear (driving gear) turns as opposed to how fast the second gear (driven gear) turns**. \\ __Now if you divide backwards instead, teeth count of the second gear divided by the teeth count of the first gear__, you'll get a number that represents how much faster the first gear is turning as opposed to the second gear. So now the formula changes and you do the math to get (40 / 20 = 2). That means the **first gear** is turning 2 times when the second gear has made 1 full turn on it's shaft. And the speeds are the same between them. The RPM of the first gear is still turning at 1000 RPM and the second gear is still turning at 500 RPM (1000 / 2 = 500). \\

**These 2 different ratios above are generally not distinguished apart from each other or at least not enough**. \\ As is shown, each result points to one or the other's gear speed although the result is to the relationship between both gears. The difference is in the calculations and which gear or gearset is being referred to. \\

**Speed Ratio**: \\
A speed ratio uses the gear ratio to find out how much faster the driven gear turns than the driver gear turns. \\
Using the inverse of the gear ratio shows how much faster the driver gear is than the driven gear. \\
As can be seen in the second drawing below, the speeds are the same even though different math was used to get there. \\ 

{{:techtalk:ref:svcproc:gear_ratio_and_inverse_ratio.png?direct&400|}} ((drawing by Hippysmack)) {{:techtalk:ref:svcproc:gear_ratio_and_speed_ratio.png?direct&400|}} ((drawing by Hippysmack)) \\
\\

**The inverse gear ratio is used to find a "mechanical advantage" of the gears paired together**. \\
(which represents a change in torque or speed where the driven gear is either smaller or larger in teeth count than the driver gear and to what degree). \\
The power from the source "is what it is" and can only be changed by more or less throttle (or engine RPM). However, that power can be manipulated to either achieve more torque or more speed (but not both) further down the gear train by changing the gear ratios. The total power stays the same, from the conservation of energy (the law of conservation of energy says that energy is neither created nor destroyed. When people use energy, it doesn't disappear. Energy changes from one form of energy into another form of energy.) ((https://www.eia.gov/energyexplained/what-is-energy/laws-of-energy.php)) \\
The mechanical advantage is a representation of leverage (or torque) gained or lost from gear ratios and is expressed in the form of a ratio. \\

**Torque vs Speed** \\
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; \\
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. \\
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 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). \\
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. 
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)) \\

**Worth noting is that the actual power source to the transmission can change during a ride**. \\
The input source to the transmission with the clutch engaged (clutch lever released) is the engine. When you are on the throttle, the motor is driving the transmission and thus the rear tire. The motor is driving the mainshaft and it's gears, and the mainshaft gears are driving respective countershaft gears and thus the rear tire. The input source to the transmission with the clutch disengaged (clutch lever pulled) is the rear tire. When you disengage the clutch, the motor is now not attached to the transmission but the transmission gears still turn. The rear tire is now driving the countershaft and it's gears which turn their respective mainshaft gears. When you let off the throttle with the clutch engaged (lever released), the rear tire is still trying to drive the transmission at the speed the motor was before pulling the clutch. So there is a push/pull going on inside the transmission while riding depending on throttle load. \\

====== Terms ======

  * **Final Drive Ratio**: \\ The final drive ratio is the last bit of gearing between the transmission and the rear wheel.
  * **Gear Ratios**: Gear ratios represent the gears’ relation to each other in size. ((https://www.artofmanliness.com/skills/manly-know-how/gearhead-101-understanding-manual-transmission/)) \\ When different sized gears mesh together, they can spin at different speeds and deliver different amounts of power. \\ When the input gear rotates, it transfers its rotational energy to the output gear. The gear ratio determines the speed and torque of the output gear. \\ Gear ratio is normally expressed as an ordered pair of numbers separated by a colon, for example, 3:1 (or 3 to 1). \\ A Gear Ratio can increase the output torque or output speed of a mechanism, but not both. ((https://mae3.eng.ucsd.edu/machine-design/gear-ratios))
    * Gear Ratio: \\ The ratio of a 2 gear train is the rate of the number of teeth on the driving gear to the number of teeth on the driven gear for our purposes. ((https://www.mechstudies.com/calculation-gear-ratio-how-calculate-explained-formula/))
    * Final Drive Ratio: The ratio between the transmission sprocket and the rear wheel.
    * Internal Gear Ratio: \\ Number of mainshaft revolutions required to drive the output sprocket 1 revolution. ((2000 HD Sportster FSM pg 6-1)) \\ This number includes all transmission gears in the selected power train but does not include the primary drive or rear wheel.
    * Speed Ratio: The speed ratio is the ratio of output speed to input speed (the inverse of the gear ratio). ((https://www.omnicalculator.com/physics/gear-ratio-speed)) \\ It is calculated the same as the mechanical advantage but the results are used differently. \\ If a 29T gear drives a 34T gear, the gear ratio is 0.85294, the driven gear turns 0.85294 turns to 1 full revolution of the driver gear. \\ Using the inverse of that, the driven gear turns 1.1724 times slower than the driver gear.
    * Overall Gear Ratio: \\ Number of engine revolutions required to drive the rear wheel 1 revolution. ((2000 HD Sportster FSM pg 6-1)) This number includes all gearing in the system (primary, transmission and final drive).
    * Primary Drive Ratio: The ratio between the crankshaft sprocket and the clutch sprocket.  
  * **Drive and Driven Gears**: Determining which is which is crucial in calculating the gear ratio. \\ Example 1: A 20T gear drives a 40T gear at a ratio of 0.5:1 - driven gear turns 0.5 (or 1/2) revolution for every 1 full revolution of the driving gear. \\ Example 2: A 40T gear drives a 20T gear at a ratio of 2:1 - driven gear turns 2 full revolutions for every 1 full revolution of the driving gear.
    * Driving Gear: \\ (aka input gear), The driving gear is the gear that transmits power.  
    * Driven Gear: \\  (aka output gear), The driven gear is the gear that receives power.
  * **Gear Train** : \\ A Gear train consists of two or more gears in series. It's application is to increase or decrease the speed or torque of the output shaft. ((https://www.smlease.com/entries/mechanism/gear-train-gear-ratio-torque-and-speed-calculation/))
  * **Input Shaft**: \\ The input shaft is the shaft that is transmitting power (the mainshaft when clutch is engaged or the countershaft when clutch is disengaged). \\ In 5th gear, the power is transferred entirely through the mainshaft at a 1:1 ratio. So in 5th gear, the mainshaft is the output shaft.
  * **Mechanical Advantage**: \\ A mechanical advantage refers to an increase (or decrease) in torque or force that a mechanism achieves through a power transmission element. Gear ratio is used to define the mechanical advantage. Mechanical advantage is a measure of the ratio of output force to input force in the gear train in this application. ((https://energyeducation.ca/encyclopedia/Mechanical_advantage)) Despite changing the forces that are applied, the conservation of energy is still true and the output energy is still equal to the input energy. 
  * **Torque Ratio**:  \\ The torque ratio is the rate of the torque of the driving gear to the torque of the driven gear. ((https://www.mechstudies.com/calculation-gear-ratio-how-calculate-explained-formula/)) It determines the torque of the system.
  * Speed Ratio: \\ The speed ratio is the ratio of the angular velocity of the driving gear to the angular velocity of the driven gear. ((https://www.mechstudies.com/calculation-gear-ratio-how-calculate-explained-formula/)) It determines the speed of the system.
  * **Speed (RPM)**: \\ The rotational speed of the shaft generated by the motor, expressed in rpm (rotations per minute). ((https://www.globalspec.com/learnmore/motion_controls/motors/gearmotors)) The shaft speed in a gearmotor is proportional to the gear ratio. The output speed can be found by dividing the input speed by the gear ratio. Gear ratios above one will reduce speed, while those below one will increase speed. Another explanation: In a simple gear system, two gears with different numbers of teeth are meshed together. ((https://www.mechstudies.com/calculation-gear-ratio-how-calculate-explained-formula/?expand_article=1)) When the input gear rotates, it transfers its rotational energy to the output gear. The gear ratio determines the speed and torque of the output gear. A gear with fewer teeth than the input gear will rotate faster and provide less torque, while a gear with more teeth will rotate slower and provide more torque.
  * **Spur Gears**: \\  The spur gears used in Sportsters have straight cut teeth positioned with mated pairs on parallel axis.
  * **Output Shaft**: The output shaft is the shaft that is receiving power (countershaft when clutch is engaged in 1st-4th gears) or (mainshaft in 5th gear).

====== Formulas ======
  * **Gear Ratio** for 2 gears = (number of teeth on driving gear) / (number of teeth on driven gear)
  * **Internal Gear Ratio** for 4 gears: (driver gear teeth x driver gear teeth) / (driven gear teeth x driven gear teeth)
  * **Speed Ratio** = (driven gear) / (driver gear)
  * **Output Speed** = (input speed) x (gear ratio)
  * **Mechanical Advantage** for 2 gears = (number of teeth on driven gear / number of teeth on driving gear)
  * **Mechanical Advantage** for 4 gears = (number of driven gear teeth x number of driven gear teeth) / (number of driver gear teeth x number of driver gear teeth)
  * **Output Torque** = (input torque) x (mechanical advantage).

====== Examples ======
The examples below all use transmission 2nd gear as a reference. \\
The drawing below shows how the gears are positioned while in second gear and can be used in reference to the examples. \\
The gears in the power flow: \\
M2 is splined to the mainshaft and is driving C2 which is sleeved over bearings on the countershaft. \\
C2 is locked to the countershaft by C3 and C5 is splined to the countershaft. C5 is driving M5 which is sleeved over bearings on the mainshaft. \\
With both C2 and C5 locked to the same shaft, the speed for both these gears are the same.  M5 is splined to the transmission sprocket and their speeds are the same. \\

{{:techtalk:ref:svcproc:1991-2003_trans-flow-2nd_by_hippysmack.png?direct&600|}} ((Drawing by Hippysmack with help from IXL2Relax with graphic design))

===== Ratios for 2 Gears Only =====
The information below shows how to calculate the numbers for a gear train using only 2 gears. \\
Instead, you can find a gear ratio calculator online to do the math for you. \\
[[https://www.omnicalculator.com/physics/gear-ratio|Click Here]] to link to one that gives you gear ratio, mechanical advantage, output speed and torque by inputting known values.

The examples below are using a MS-2 (29T) and a CS-2 (34T) gearset (or gear train). Engine RPM at constant 1000 and initial torque of 50 ft/lbs. \\
In this gearset, M2 is splined to the mainshaft, turns the same speed as the mainshaft and serves as the driving gear of the set. \\
C2 is sleeved over bearings on the countershaft, has to be coupled to the countershaft by the dogs on C3 gear and serves as the driven gear to M2. \\ 
These are arbitrary combinations just for example. \\


  * **Gear Ratio** = (number of teeth on driving gear) / (number of teeth on driven gear)
    * Example: A 29 teeth gear is driving a 34 teeth gear at a ratio of 0.85:1 \\ Plug the numbers into the formula (29 / 34) = 0.85294 (or 0.853) \\ The result is expressed in ratio as 0.853:1 (or 0.853 to 1). \\ In this example, CS-2 turns (slower) and at 0.853 times for MS-2 to turn 1 full revolution.  \\ While this setup shows a gear reduction in terms of speed, it creates an output that has more torque when compared to the input torque between these 2 gears.
  * **Output Speed** = (input speed) x (gear ratio)
    * Example: Given a mainshaft speed of 1000 rpm using the gear ratio above (0.853), the countershaft speed is 853rpm \\ Plug the numbers in the formula (1000 x 0.853) = 853 \\ In this example and with a constant input rpm, the countershaft (by way of CS-2) has a speed of 853 rpm.
  * **Mechanical Advantage** = (number of teeth on driven gear / number of teeth on driving gear)
    * Example: A 34 teeth gear is being driven by a 29 teeth gear at a mechanical advantage of 1.172:1 \\ Plug the numbers into the formula (34 / 29) = 1.172413793103448 \\ In this example, the result is expressed in ratio as 1.172:1 (or 1.172 to 1). \\ This example gives 0.172 times more output torque as compared to the input torque between these 2 gears.
  * **Output Torque** = (input torque) x (mechanical advantage).
    * Example: Given an input torque 50 ft/lbs, the output torque will increase to 58.6 ft/lbs @ 1000 RPM between the example gears \\ Plug the numbers into the equation (50 x 1.172) = 58.6 \\ In this example, the torque from the mainshaft was increased on the countershaft by 8.6 ft/lbs (by way of CS-2). 

===== 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). \\
However, Sportster transmissions have a 1:1 ratio 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. \\

This section shows how to calculate internal ratios for yourself. \\
**You must already have gear teeth counts for all the gears in the transmission to calculate the internal ratio**. \\
You can find a gear ratio calculator online to do the math for you if desired but you still need all teeth counts to use it. \\ 
[[https://evolventdesign.com/pages/gear-ratio-calculator|Click Here]] to link to one that gives you internal gear ratio and output speed by inputting known values. \\ 

The information below shows how to calculate the numbers for Transmission GEAR 1st-4th. These all use 4 gears (2 drivers and 2 driven) to turn the transmission sprocket. \\
The engine sprocket and clutch sprocket is not included since they are part of the Primary Drive Ratio which is calculated separately.
The transmission sprocket and rear wheel sprocket is not included in these calculations since they are part of the Final Drive Ratio which is calculated separately. \\

**The internal ratio, (AKA, gearbox ratio), includes the mainshaft and countershaft gears that are in the power flow for the transmission GEAR selected**. \\
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. \\ 

==== Example ====
This example uses the stock gears from a 1998 XL1200; M2 (29T) - C2 (34T) gearset and C5 (25T) - M5 (42T) gearset. \\
M-2 gear is driving C2 gear and C5 gear is driving M5 gear. Use the __inverse gear ratio__ for each gearset. \\
You may see the word "gear ratio" elsewhere but this article wishes to distinguish the difference for clarity. \\
Using the inverse ratio, the result will show the amount of torque gained or lost in the listed internal gear ratios per GEAR selected. \\

  * **Inverse Gear Ratio** = (driven gear teeth x driven gear teeth) / (driver gear teeth x driver gear teeth)
    * Assemble gear teeth count for each gearset:
      * Driven Gears: C-2 (34T) and M-5 (42T)
      * Driver Gears: M-2 (29T) and C-5 (25T)
    * Plug the numbers in the formula: 
      * (34 x 42) / (29 x 25) or (1,428 / 725) = 1.969655172413793
      * The result is expressed in ratio form (1.969655172413793:1)
    * **The Internal Gear Ratio** for a stock 2nd GEAR on a 1998 XL1200 is 1.969655172413793:1 \\ You can round that ratio up to 1.970:1 or use HD's rounded down ratio of 1.969:1 but using the full figure above will be the most accurate for further calculations if needed.

{{:techtalk:ref:svcproc:gear_ratio_and_internal_ratio_by_hippysmack.png?direct&600|}} ((drawing by Hippysmack)) \\
\\

Next, you run the numbers using the same formula for the other 3 gearsets. And of course 5th gear ratio is 1:1. \\
And you end up with a list of numbers as shown in the chart below (with HD's numbers listed).
Looking at the chart, you can see the torque decrease as you go up thru the gears. \\
Higher internal ratios = higher output torque and lower speed. Lower internal ratios = lower output torque and higher speed. \\

|**Internal Ratio \\ 1998 XL200**|1st GEAR|2nd GEAR|3rd GEAR|4th GEAR|5th GEAR|
|:::|2.685:1|1.969:1|1.433:1|1.178:1|1:1|

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. \\

Based on KHK information ((https://khkgears.net/new/gear_knowledge/the-first-step-of-mechanism-design-using-gears/know-about-gear-transmission-torque.html)) , we'll just use an efficiency rate of 99% for spur gears. \\
In order to find approximate Actual ratio, the formula needs to be altered. \\
  * **Inverse Gear Ratio** = 0.99 x (driven gear teeth x driven gear teeth) / (driver gear teeth x driver gear teeth)
    * 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.

===== Primary Drive Ratio =====
The primary ratio is calculated between the engine's crankshaft sprocket and the transmission clutch sprocket. \\
This example uses an engine sprocket with 35 teeth and a clutch sprocket with 56 teeth. \\
The formula uses the inverse of the gear ratio formula and the result gives the primary torque ratio, not speed. \\

  * **Inverse Gear Ratio**: (driven gear) / (driving gear)
    * Assemble teeth count:
      * Clutch sprocket (56T)
      * Engine sprocket (35T)
    * Plug the numbers in the formula:
      * 56 / 35 = 1.60
      * The result is expressed in ratio form (1.60:1)
  * **The Primary Ratio** for a stock 1998 XL1200 is (1.60:1) which results in a gain in torque (loss in engine speed) at the clutch sprocket. 

{{:techtalk:ref:svcproc:gear_ratio_and_primary_ratio_by_hippysmack.png?direct&600|}} ((drawing by Hippysmack)) \\

===== Final Drive Ratio =====
The final drive ratio is calculated between the transmission output sprocket and the rear wheel. \\
This example uses a transmission sprocket with 29 teeth and a rear wheel sprocket with 61 teeth on a 1998 XL1200 Sportster. \\
The formula uses the inverse of the gear ratio formula and the result gives the final drive torque ratio, not speed. 

  * **Inverse Gear Ratio**:  (driven gear) / (driving gear)
    * Assemble teeth count:
      * Rear wheel sprocket (61T)
      * Transmission sprocket (29T)
    * Plug the numbers in the formula:
      *  61 / 29 = 2.103448275862069 (or 2.103)
      * The result is expressed in ratio form (2.103:1)
  * **The Final Drive Ratio** for a stock 1998 XL1200 is (2.103:1) which results in a gain in torque (decrease in speed) at the rear wheel. \\ It is listed 2.10:1 in the FSM.

\\
{{:techtalk:ref:svcproc:gear_ratio_and_final_drive_ratio_by_hippysmack.png?direct&600|}} ((drawing by Hippysmack)) \\

===== Overall Gear Ratio =====
The overall gear ratio is calculated for the entire gear train in the system including primary, transmission and final drive ratios. \\
Each of those 3 ratios are calculated using the Inverse Gear Ratio to reveal the TORQUE RATIO.
This example uses the calculations above for each of those parts of the gear train. \\

  * **Overall Gear Ratio**: (primary ratio) x (internal ratio) x (final drive ratio)
    * Assemble the 3 torque ratios needed:
      * Primary gear ratio (1.60:1)
      * Transmission 2nd GEAR Internal Ratio (1.970:1)
      * Final Drive Ratio (2.10:1)
    * Plug the numbers into the formula
      *  1.60 x 1.970 x 2.10 = (6.6192) 
      *  The result is expressed in ratio form (6.6192:1)
  * **The Overall Gear Ratio ** for a stock 1998 XL1200 is (6.6192:1) which results in a gain in torque (decrease in speed) at rear wheel. \\ The overall GEAR ratio is listed in the FSM as 6.62:1 for a 1998 1200 Sportster second GEAR.
\\

{{:techtalk:ref:svcproc:gear_ratio_and_overall_ratio_by_hippysmack.png?direct&700|}} ((drawing by Hippysmack)) \\


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