Anyone good with gearbox maths?

[Firefly90]

Basicly im doing an assignment for my motorsports degree and here is what the questio says

"You have been asked to provide a specification for a race transmission. The engine produces peak power of 500kW at 12,000 rpm and useful power from 8,000rpm. The transmission must be a 6 speed type with integrated final drive and should give a projected top speed of 220mph on 16-26 /15 rear tyres. You should specify a set of gear ratios, with projected top speeds in each gear, and a final drive ratio, giving reasons for your choices."

Basicly i need to work out the ratios for the gears. Tho im a bit stuck on finding out the primary ratio for a forumla

Overal ratio = Primary Ratio x Gear Ratio x Final drive Ratio

I've allready managed to work out the Final drive ratio as 4.22:1 and the 6th gear ratio as 1:1 but i can't seem to get primary ratio which is kinda crutial to the rest of my calculations.

Any Ideas???

 

[narf]

So your tyres are 66cm in diameter, 207cm in circumference, and you need to achieve 98.3m/s in 6th at 200rps? at 4.22:1 overall ratio for 6th gear.
How you distribute that ratio between final drive and gearbox doesn't really matter. Picking 1:1 for 6th makes some beauty-sense, so final drive of 4.22 it is.
Now, idunno whether you have some strategies on distributing the other gears in class, but here's mine: You know you can use your engine from 8000rpm. When accelerating through the gears, you would shift up at 12000rpm and ideally get 8000rpm in the next gear. In other words, top speed in 5th would be 2/3 of the top speed in 6th. Following that strategy you would get these top speeds:
98.3, 65.5, 43.7, 29.1, 19.4, and 12.9 in first.
Matching gears to a track you could say 2nd at 8000rpm matches the Loewe's hairpin in Monaco :lol: so you can accelerate out of it in 2nd from the bottom of your useful power range :lol:

 

[Firefly90]

Now, idunno whether you have some strategies on distributing the other gears in class, but here's mine: You know you can use your engine from 8000rpm. When accelerating through the gears, you would shift up at 12000rpm and ideally get 8000rpm in the next gear.

I think that is what my lecturer said in an e-mail he sent but i was a bit confused as to where to get the inital values from. I've since figured out that primary ratio i.e. engine to gearbox input, must also be 1:1 since overal ratio and final ratio are the same.

I found that using the gear ratio in 6th, 8000rpm would produce a road speed of 146.7 mph through a series of calculations so that would be the top speed of 5th and then i work out what the ratio is need to produce that road speed at 12000 using 4.22:1 as final drive and 1:1 as primary ratio.

 

[narf]

That series of calculations would be multiply 220mph by 2/3? :lol: (8000rpm in 2/3 of 12000rpm) But yeah, work out how to achieve 146.7mph at 12000rpm to get the 5th gear ratio. Once you have worked it out, click the spoiler to verify

Spoiler

1.5:1 or the reciprocal of 2/3.

Total ratio in 5th then is 4.22*1.5:1, 6.33:1. At 6.33:1, 200 engine revolutions per second translate to 31.6rps at the wheel. Your wheel circumference is 2.074m, so that's 65.6m/s at 12000rpm in 5th. Purrfect, exactly 2/3 of 98.3m/s (220mph).

 

[MadCat360]

Following that strategy you would get these top speeds:
98.3, 65.5, 43.7, 29.1, 19.4, and 12.9 in first.

That looks pretty backwards to me. You've got your driver shifting into 3rd gear at 42 MPH! Why've ya done that?

 

[narf]

That looks pretty backwards to me. You've got your driver shifting into 3rd gear at 42 MPH! Why've ya done that?

Because the assignment states useful power from 8000rpm, and my strategy is explainable using that factoid. Whether it's fastest for real cars with real engines on real tracks is another story. As a student you could ignore the hint given and shift up to 9000rpm instead, then you'd go into third at 31.1m/s.

However, to explain this ignorance of hints to your teacher you would have to know the exact power curve of the engine... which we don't. For all we know, it could have max torque at 8000rpm resulting in pretty much equal power all the way from 8000rpm to 12000rpm.

 

[Blythy]

There are two ways to design a gear box -

Both start with your Top Speed: Which you have already defined for you.

Your next choice is your first gear, which is generally hill climb force, which is kinda redundant for this. So just ignore that bit.

The variance in the method is your inbetween ratios: You can either go for a constant ratio difference (which is stupid and shit) or you can go for a constant speed difference (which is far far better)

Now, idunno whether you have some strategies on distributing the other gears in class, but here's mine: You know you can use your engine from 8000rpm. When accelerating through the gears, you would shift up at 12000rpm and ideally get 8000rpm in the next gear. In other words, top speed in 5th would be 2/3 of the top speed in 6th. Following that strategy you would get these top speeds:
98.3, 65.5, 43.7, 29.1, 19.4, and 12.9 in first.

with respect, you're talking out of your arse. You've not taken into account anything about the power or torque of the engine. You've done the constant ratio difference thing and got things arse about face. Why would you be doing 147 mph to 220 mph when you've got the least torque at the wheels from the engine, when it's easily possible to be doing part of that with a lower gear ratio.

The 'useful power' thing is a bluff, designed to throw you (it's the second stage, not the first). No car would design a gearbox with a constant ratio difference, it would be undriveable. Get a copy of autocar, and look at the gearbox ratios of the car being road tested. Every car will show the gear ratios getting closer and closer together as you move up through the gearbox.

Here's your strategy: Decide your top gear overall ratio (this is pretty much done for you)
Decide your top speed in 1st.
Equally space the top speed in each of the gears between 1st and 6th.
Work out the ratios of the inbetween gears.
check that at top speed in 1st, when you change, the engine speed is over 8000 in second, and the same for moving from top speed in second to third, etc all the way up to 6th.
if this isn't the case, tune your top speed in 1st. and redo the process.

Now that you have your gear ratios, think of how the gearbox is designed: Remember, the bigger the ratio, the physically bigger the gears have to be (And these gears are going to have to heavy duty to begin with to transmit 500kW of power), any way you can think of REDUCING (say for instance, the primary reduction gear) the gearbox ratios will help save weight in the gearbox as well as inertia in the drivetrain.

 

[Firefly90]

In response to Blythy, your reasoning is very good... however, this is a qoute from and e-mail from my lecturer on calculating the ratios:

"Work out a ratio for top gear to give the required speed at 12000 rpm. Assuming that`s 6th gear, work out the road speed at 8000rpm with that gear ratio, then choose a ratio that gives that same road speed at 12000 rpm - that`s 5th gear. Continue for another four gears." ...which is the same strategy as narf.

Im not saying that Blythy is wrong or that narf and my lecturer are right but i think im gonna stick with how i've done it already.

 

[narf]

with respect, you're talking out of your arse. You've not taken into account anything about the power or torque of the engine. You've done the constant ratio difference thing and got things arse about face. Why would you be doing 147 mph to 220 mph when you've got the least torque at the wheels from the engine, when it's easily possible to be doing part of that with a lower gear ratio.

Why do I not take engine characteristics into account? Because there is no info on the engine characteristics apart from "use the 8000 to 12000 rev band". That's exactly what I did.

For example, the engine might be similar to this:

https://pic.armedcats.net/n/na/narf/2011/01/23/M_motor.jpg

It produces the same amount of power from 4500rpm to 6500rpm. Scaled up to a 12000rpm engine this range would be 8307rpm to 12000rpm - almost exactly what the assignment suggests, use the range of 8000rpm to 12000rpm. With my gearbox ratios, no matter what speed you drive you always get the maximum power.

Remember, he needs to reason why he chose the ratios he chose. He could base his ratios on the facts given in the assignment, or he could make stuff up about engine characteristics (or, as you would put it, talking out of his arse).

 

[Blythy]

In response to Blythy, your reasoning is very good... however, this is a qoute from and e-mail from my lecturer on calculating the ratios:

"Work out a ratio for top gear to give the required speed at 12000 rpm. Assuming that`s 6th gear, work out the road speed at 8000rpm with that gear ratio, then choose a ratio that gives that same road speed at 12000 rpm - that`s 5th gear. Continue for another four gears." ...which is the same strategy as narf.

Im not saying that Blythy is wrong or that narf and my lecturer are right but i think im gonna stick with how i've done it already.

If your lecturer is giving you that advice, he's an idiot.

play with this: http://www.fatboyraceworks.com/gears/ and notice how the speed differences are constant.

once you've done your ratios, put them in there, and compare.

And seriously think about what your lecturer is asking you to do from his email. Would you really honestly want to waste all of the lovely tractive effort that engine has getting to 65 mph in the first three gears, and then spend the next three gears with lower tractive effort doing the remaining 155 mph to 220? Think of it in a drag environment - there's no point in getting to 60 in 2 seconds if your time to 100 is 40 seconds.

 

[narf]

Would you really honestly want to waste all of the lovely tractive effort that engine has getting to 65 mph in the first three gears, and then spend the next three gears with lower tractive effort doing the remaining 155 mph to 220?

Assuming the 1.8TSI, the power is the same throughout the rev range used. Hence there is no way to get more power from the engine, and no need to do the gearbox any other way.

 

[MadCat360]

IMO your lecturer should have given you a dyno sheet of a real race engine, drag values, wheel sizes etc and told you to optimize the transmission for ideal acceleration to max speed. A pretty standard practice. This is just really vague.

 

[Firefly90]

IMO your lecturer should have given you a dyno sheet of a real race engine, drag values, wheel sizes etc and told you to optimize the transmission for ideal acceleration to max speed. A pretty standard practice. This is just really vague.

It does seem a bit vague i agree. This is my 1st year i guess, and its only a FdEng which is the equivilant of a HND, dunno what the German and US equivalents are.

 

[narf]

IMO your lecturer should have given you a dyno sheet of a real race engine, drag values, wheel sizes etc and told you to optimize the transmission for ideal acceleration to max speed. A pretty standard practice. This is just really vague.

Depends on the goal of the assignment. If you want experienced students to evaluate every aspect then yes, the more info the better. If you're dealing with beginners and only want to teach them about gear ratio maths then less info can focus them on the task at hand.