if you have ever ridden a bike you'll know it's very difficult to start pedaling in a high gear so we need to start in a low gear to get the bike moving at a certain point our legs are spinning very fast but we can't go any faster so we need to change to another higher gear once we reach a steep hill we need to move to a lower gear the same with a car we start in our lowest gear number and work our way up as the vehicle increases in speed then we change down as we drive up a hill a low gear provides low speed but high torque a high gear gives high speed but low torque torque is a measurement of the force which causes something to rotate around a point think of a wrench and a nut which has seized up using a small wrench is very hard to free the nut using a long wrench will make it much easier I that's because of torque if we used a 30 cm wrench and applied 90 Newtons of force we have 0.3 M multiplied by 90 Newtons which gives us 27 Newton M of torque however if we applied the same 90 Newtons of force to a wrench that was 60 cm long then we would get 0.6 M multiplied 90 Newtons which gives us 50 4 newon M so from this simple formula you can see we have more force acting on the nut by using a longer wrench essentially we're using a larger Circle to turn a smaller Circle by changing the size we change the speed and the torque if we were to connect two gears and rotate one of them then the other gear would also rotate if we attach the engine to the first gear then this will be the driver gear and the another gear is therefore the driven gear when the two gears are the same diameter we have a 1:1 ratio which means every time the driver gear completes a full rotation The Driven gear also completes one rotation so the output speed is the same as the input speed if the driven gear is half the diameter of the driver gear then we have a 1:2 ratio which means for every full rotation of the driver gear The Driven gear completes two full rotations this means the driven gear is rotating much faster if the driven gear is twice the diameter of the driver gear then we have a 2:1 ratio which means for every one full rotation of the driver gear The Driven gear rotates only half a turn so we need the driver gear to rotate twice to complete a full rotation of the driven gear notice that the driven gear rotates the opposite way this is basically a reverse gear in order to make the output rotate in the same direction as the input we need to insert another gear which creates something known as a gear train the middle gear is known as an idler gear we could add many gears side by side to change the speed and also the output Direction but this will take up a lot of room so instead we can mount gears to the same axis and create a compound gear drain this will do the same job but it will take up far less space let's look at how to calculate the RPM and torque of simple gear drains by the way you can download an Excel sheet of these calculations links can be found in the video description for those we're going to use the formulas ratio equals teth of the output gear divided by teth of the input gear RPM output equals the RPM input divided by the ratio and finally torque output equals the ratio multiplied by the torque input for example if gear a has 8 teeth and gear B has 10 teeth the ratio is 10 / 8 which is 1.25 if gear a rotates at 150 RPM then 150 divided by 1.25 = 120 RPM if gear a has a torque of 20 n m then 1.25 multiplied by 20 gives us 25 new M this gear will rotate the opposite way to gear a it will rotate slower because it is larger but it will have more torque if we add gear C with 20 teeth the ratio is 20 / 10 which gives us two the RPM output is 120 RPM from gear B divided by 2 which gives us 60 RPM the torque is going to be 2 multiplied by 25 new M from gear B this will give us 50 Newt M so this gear will rotate the same direction as gear a but it will rotate slower because it is larger although it will have more torque if we were to add gear d with 8 teeth then the ratio is 8 / 20 which gives us 0.4 the RPM is 60 RPM from gear C divided by the ratio of 0.4 which gives us 150 RPM the torque is 0.4 multiplied by 50 new M which gives us 20 Newt M so this gear will rotate the opposite way to gear a but it is the same size so so it will rotate at the same speed and the same torque although this doesn't take into account any losses which we would see in the real world so this setup lets you visualize how gears manipulate speed torque and Direction what if we had a compound gear train like this which has the same size gears the same input torque and the same rotational speed again links in the video description for the Excel sheet calculator for this so with this setup we have four gears a b c and d but B and C are compound if gear a has 8 teeth and gear B has 10 teeth then the ratio is 10 / 8 which is 1.25 gear a rotates at 150 RPM so gear B is 150 RPM divided by 1.25 which gives us 120 RPM gear a has a torque of 20 Newt M so gear B is 1.25 mtip by 20 n m which is 25 Newton M so this gear rotates the opposite way to gear a it will rotate slower because it is larger but it has more torque if gear C has 20 teeth then the ratio is 20 / 10 which is two the RPM is going to be the same as B which is 120 RPM because these two gears are compound and share the same shaft the torque is also going to be the same as B so it's 25 Newton M this gear also rotates the opposite direction to gear a it will rotate slower than gear a because of the size of gear B and it will also have less torque than gear a again because of gear B if gear D has 8 teeth then the ratio is 8 / 20 which is 0.4 the RPM is 120 RPM from gear C divided by 0.4 which is 300 RPM the torque is 0.4 multiplied by 25 NT M from gear C which equals 10 Newt M so this gear rotates the same direction as gear a it rotates faster but with less torque so we need to consider the application of the gearbox how many gears are connected and what torque and speed we require okay that's it for this video but to continue learning about mechanical and automotive engineering check out one of the videos on screen now and I'll catch you there for the next lesson don't forget to follow us on Facebook Twitter Instagram LinkedIn as well as the engineering mindset.com