Everything you ever wanted to know about gears

Discussion in 'SN95 4.6L Mustang Tech' started by Slider, Apr 26, 2004.

  1. There have been a lot of misconceptions about gears floating around, and I would like to provide what knowledge I have about them.

    First, changing to something like a 4.10 gear does indeed increase torque at the rear wheels, but as a consequence the rate/speed/rpm that this force/torque can be applied at decreases by the same ratio. If the torque multiplication goes up 10%, then the speed for that given torque goes down 10%. This is a physical law of gear trains. Also, the overall power to the rear wheels is the same (this is not exactly true, but it will be covered later) since you have not actually done anything to the engine to make more power. So, you can also look at it like this:

    Power = Torque*RPM/5252
    If the power must stay the same
    RPM = Power*5252/Torque
    RPM = (constant value) /Torque
    Then as the torque goes up, then RPM goes down.

    Now that means that adding gears will not make your car faster over a given distance if you only use ONE gear. You maybe able to accelerate fast at first, but you cannot go as fast so in the end you cover the same distance in the same time.

    However, when multiple gears are used, such as provide by the transmission, then you can go faster. The reason why is that you can think about the power curve of an engine is shaped like a bell. When you only use one gear you only have the power output of this one curve over your entire distance you travel. You will start out low on power and increase in power until you hit your peak power, and then it will decrease again. The amount of power you use over the entire distance is not just the peak power, but it is the average power. That is why you always here about racers saying that peak power is not always that important. As you added more gears you can keep reusing this power curve multiple times, but at the cost of less torque due to the gearing. First gear will give you the torque to get the car accelerating, but the other gears help you obtain higher speeds. Now, you can average the power you used over the distance. As you use more gear ratios over the same distance your average power used actually increases. This is what makes your car faster with 4.10 gears. Instead of using 1st, 2nd, and 3rd gear in the quarter mile you are now also using 4th gear. More times through the engine’s power band means more average power used, and that means you can go faster.

    Now that you understand on how gears actually make your car faster, then let me make a comment about the dyno. Your car’s engine is “basically” making the same amount of power no matter what gear ratio you run. The fact that the dyno reads a different value with different gears is due to how the power is measured. You are not directly measuring the engine’s power on the dyno, but you are instead measuring the power applied to the dyno or the rear wheel horse power (rwhp). There can be two causes for a lower rwhp reading. The most common loss of hp is due to drivetrain efficiency. This is how much power is used/lost due to the transmission and rearend gears. This power is used to basically overcome friction and usually shows up as heat, but is also a function of how much “slip” there is present in the drivetrain (i.e. clutches and converter). How much power is lost varies depending on the transmission type, gears types, and gear ratios. This is where you get the numbers of 15% (5 spd) and 20% (auto). Basically 15% of the power your engine produces is wasted to overcome friction in the gears, and simple gets transformed into heat. This is not really constant, but for this discussion it is easier to see it that way.

    Now, when you switch to something like 4.10’s in the rear end it is noted that the dyno shows a loss in hp. Well, this is true and it really does have some to do with the drivetrain loss, but not all. You will loss a very small amount of power due to that lower gears are a little less efficient, but it is very little and not enough to worry about. Where the real power loss comes in is due to how much faster you car can accelerate the rear wheels. The power measured by a dyno is determined from drums acceleration, speed, and inertia:

    Power = Torque*(Angular Velocity) => this is where hp= tq*rpm/5252 comes from.
    Torque for a rotating system is calculated as: Torque = Inertia*(Angular Acceleration)
    Thus, Power = Inertia*Acceleration*Velocity

    P = I*A*V

    However, this does not include the inertia of the car’s parts such as the driveline components (flywheel, clutch, transmission parts, rear end, driveshaft, wheels, etc). All these things are gong to require power to accelerate them also. Technically the equation would look something like this:

    Power(dyno) = Power(engine) – Power(driveline)

    Power(dyno) = Power(engine) – I(flywhl/cltch)*A(flywhl/cltch)*V(flywhl/cltch) – I(trans)*A(trans)*V(trans) – I(wheels)*A(wheels)*V(wheels) – etc.

    So technically the dyno only measures velocity and acceleration not torque or power. The computer attached to the dyno calculates the torque and power using the known inertia of the dyno’s drums and an estimate of what you car’s driveline inertia.

    This brings up a good point while I am here. One cannot take the result from the dyno as gospel to how much power you are making. The last bit about you car’s inertia is important. Depending on the values used in the computer’s calculation for you car’s inertia can affect the dyno’s reading, and it is different for every car and truck. Since it is impossible to measure all these values the dyno just uses an estimate. I have heard of some dyno operators using the wrong values to make it look like you have a little more power than you really do. However, in general the idea is that the dyno’s drum has an inertia that is much great than you car’s as to reduce the effects of the car’s driveline inertia on the power readings.

    Ok, now to the part about different dyno readings in different gears. The reason that you will see lower power readings with lower gears (1st or 4.10’s) is because they accelerate the whole engine-driveline-drum system faster. For a simple example let’s look at changing from 3.27’s to 4.10’s dynoed 4th gear (1:1).

    engine => 4000 rpm
    trans => 4000 rpm
    wheels => 4000/3.27 = 1223 rpm

    engine => 4000 rpm
    trans => 4000 rpm
    wheels => 4000/4.10 = 976 rpm

    Looking at the above we can see that changing from 3.27’s to 4.10’s decreased the wheels rpm by 247 rpm or 1.25%. Going by just the wheels’ rpm and gearing the power output should stay the same since the torque/acceleration went up by 1.25%, but the rpm/velocity went down by the same 1.25%.

    The important difference is that the engine and transmission rpm is the same, yet they where accelerated faster as a result of the 4.10 gears. That is it took less time to get up to 4000 rpm with the 4.10’s then it did with the 3.27’s. This means that it takes more power to accelerate the engine and driveline components since the velocity is the same, but we have a higher acceleration (refer to the earlier power equation).

    Example: P(dyno) = P(engine) – P(driveline)
    3.27 => P(dyno old) = P(engine) - I*A*V
    4.10 => P(dyno new) = P(engine) - I*{4.10/3.27}*A*V = P(engine) - {4.10/3.27}*I*A*V = P(engine) - 1.25*P(dyno old)

    The change in the dyno or rwhp should look something like this:
    Pwr(4.10) = Pwr(engine) – 1.25*Pwr(3.27)

    Each part in the driveline system requires 1.25 times as much power to be accelerated when switching to the 4.10 gears. Thus the power seen at the dyno’s drum will reflect this loss.

    I hope that helps. I can’t say everything I described is 100% correct (feel free to correct me if I am wrong), but to the best of my knowledge the above should be true.

  2. But tell us how they REALLY work :rlaugh: informative post thanks!
  3. Okay.. so by switching to steeper gears from 3.27 to 4.10, your car actually accelerate faster. That we already know. Because your engine will go through the power band faster than usual producing more average hp than before. But it does not make the car produce more power.. You're just making the same power faster with steeper gear that is all.

    For the dyno part, there are many factors that come into play in order to produce the perfect numbers.. so you might see some gains and losses.

    However, I still don't quite get this part:

    "Each part in the driveline system requires 1.25 times as much power to be accelerated when switching to the 4.10 gears. Thus the power seen at the dyno’s drum will reflect this loss."

    Did that sum it up pretty nicely..? :shrug:
  4. Excellent post. I've tried to explain to many people how gears swaps affect your car but all I can say is my butt-o-meter gives them a :thumbsup:
  5. So what you're saying is my dyno #'s woulda been higher if i didn't have 4.10's?
  6. does the Dyno calibration not take into account the gearing of the Tranny and the rear end
  7. It takes power to get an object moving. The more inertia an object has the more power it takes to get it moving. It is also true that if the inertia is constant, then it takes more power to accelerate it faster.

    Just for the sake of fun. The derivative of acceleration is "jerk," seriously it is. Basically how fast you accelerate is its jerk. The more jerk the faster you accelerate :D

    Any how, changing to 4.10's is the case where you are accelerating the same inertia faster, and thus it requires more power to do so.

    If the driveline had no inertia then this would not happen. This is also the reason that some people see an increase in rwhp when they switch to an aluminum flywheel or driveshaft.
  8. We are only talking a few rwhp. Maybe 3-5 rwhp, but I would not worry about it. The benefits of the increased average power greatly out ways this little loss.
  9. The dyno only uses the exact tranny and rear end gearing to convert the dyno's drum speed to rpm.

    From what I have heard the dyno does estimate the power lost to inertia, but I do not know that for sure. It is just what I have heard. Any ways, if they do it, it is just an estimate since it cannot be directly measured for your car. I guess you could call it a fudge factor if it is used.
  10. cool info
  11. Now that's what I call an informative post. Thanks for taking the time Slider.
  12. I left this part out, and maybe I should include it for clarification. The power lost to the inertia is in addition to the power lost to the gear train's friciton/effecience.

    Power(dyno) = Power(engine) – Power(driveline inertia) - Power(driveline fricition)

    Power(driveline fricition) is typically "estimated" at a "constant" 15% to 20% of Power(engine).
  13. I'd like someone to explain to me why the trap speed with gears doesn't increase. So gears make you accelerate faster, and get to 100 faster but not increase your speed through the traps? I don't get it. I guess since you're only running for 13.5 secs instead of 14.0, you're spending less time between the lights but still trapping the same because you're able to get there faster. :shrug:
  14. i get assigned things to read in school that were shorter--where are the cliffnotes :mad:

    well looks like i have something to do tonight thanks slider :)
  15. Cool, just kinda curious not really worried. The DOHC likes the higher rpms anyway. But just so i'm clear, that loss in rwhp is just what the dyno reads, not actual loss, right?
  16. I'm pretty sure thats it.
  17. sweet post, thanks for the info. gonna pass this thread along to a couple friends.
  18. very very informative, thanks for the post it answered many questions that i had. someone should sticky this or something, might be very helpful to people out there...