Simple torque formula? (how to build a power system)

[jawnn]

This is for building a 5-600lb velomobile.

Basically I wan to drive 550lbs up the a 16% grade (max for 50ft) at about 5mph, that’s going to be about 200 rpm with a 2 to 1 gear reduction (16 sprockets on the motor 34 on the axle) on my 20” drive wheel.

So what do I do with 550lbs…16%…and 200 rpm?

I might be able to reduce the gear twice for a 400-rpm? But I am going to look for a gear motor, or at last an 1800-rpm motor.

[chuck]

Jawnn,

This is a simple problem. If it is broken down properly. I wrote a whole paper that covered all of this called physics, but I wrote it in the general discussion area and it was deleted.

Ok, We have the following
16% grade
5 mph
550 lbs

There are 3 forces that need to be overcome,
The force of gravity
The force of drag
The rolling resistance

Force of gravity is the slope x The weight
.16 x 550lbs = 88 lbs

The force of drag is 1/2 x frontal area x coefficient of drag x density of air x velocity^2
Physic students have been dropping things off of high buildings for hundreds of years, bicycle type objects generally have a coefficient of drag of about .9
The density of air is about .0728 lbs/cubic foot. Divide this by gravity which is about 32 feet/sec^2 gives us about .0023 slugs per cubic foot.
The velocity needs to be converted to feet per second. 88 feet/sec = 60 mph. soo... 5mph/60mph x 88ft/sec = 7.3 feet/sec
My frontal area is about 8 feet squared on my ride, close enough for this exercise.
Force of drag = 1/2 x 8 x .9 x .0023 x 7.3^2 = .44 lbs

Force of rolling, I think I measured coefficient of rolling at about .005 lbs, close enough for now, I will look through some old notes to see if I can find it. This did include my drive chain and motor, so it was pretty accurate.
The force of rolling is = the coefficient x (1- slope)(weight) = .005 x .86 x 550lbs = 2.4 lbs,, I think this is a little high, for some reason I think I have about a pound of rolling resistance.

We have 3 forces, add them up
Force of drag + force of rolling + force of gravity = .44 lbs + 2.4 lbs + 88 lbs = to about 91 lbs of force.

Power is Force x Velocity. Still with me?
The velocity we calculated above to be 7.3 feet/sec

Power is force x velocity is = 91 x 7.3 = about 665 foot pounds/sec

1 horsepower = 550 ftlbs/sec
665/550 = 1.2 hp required

We need to convert this to watts. 746 watts = 1 hp.
1.2 hp/1hp x 746watts = to about 900 watts at the wheel

chuck

[chuck]

jawnn,

Let me get this straight,
20 inch wheel
34 tooth wheel sprocket
16 tooth motor sprocket

Motors are in revolutions per min, so we need to calculate a wheel rpm, we must keep our units consistent.

A 20 inch wheel has a diameter of 20inches/12inches x1 foot of 1.67 feet
the wheels circumference is pi x 1.67 = 5.236 feet

Now the velocity of 7.3 feet/sec needs to be converted to feet/min

7.3ft/sec x 60sec/min = 438 feet/min

Find the rpm of the wheel divide the velocity of 438 ft/m by the circumference of the wheel which is 5.236 feet
the rpm of the wheel is 438/5.236 = 83.65 rpm

Find your motor rpm
Your reduction ratio is 34/16 .

the rpm of the motor is the wheel rpm x the reduction ratio = 83.65 x 34/16 = 177.76 motor rpm

If you ask, I will calculate the tension on the chain, this is chain breaking tension, just so you know. I would not build this with this reduction ratio , in other words, it is bad reduction design.

chuck

[swbluto]

My simulator. 'Nuff said.

[chuck]

Jawnn,

I just looked up in my Morse bearing and chain book, #40 chain at 100 rpm and a 16 tooth drive sprocket will handle .65 hp at 100 rpm and will handle 1.2 hp at 200 rpm.

chuck

[jawnn]

'Loquin' says that "this 665 foot pounds is more torque than a cummins diesel"...

Are you sure that this is right?

It's all beyond my brain power, but that does seem a bit high.

[rkosiorek]

it is not 665 ft/lbs of torque. torque is just force and distance. he is saying it is 665pound-feet per second. which is a unit of power or work done. that is a totally different animal than torque. one horsepower is equal to 550 pound-feet per second. which is the amount of energy expended to move a weight of 550lb 1 foot in 1 second. pound-feet per second is just a different method of expressing horsepower and not torque. 665pound feet per second is equal to 1.2Horsepower.

like chuck says it is just physics. and you are confusing the units of measure and what is being measured. which is easy to do if you miss or stop paying attention before you get to that very important "per second" part.

rick

[Chalo]

I just looked up in my Morse bearing and chain book, #40 chain at 100 rpm and a 16 tooth drive sprocket will handle .65 hp at 100 rpm and will handle 1.2 hp at 200 rpm.

Ordinary bicycle chains, even the thin 10- and 11-speed kinds, handle surges of several horsepower every day (usually with a bigger driving sprocket). Remember that pedaling force comes in shoves separated by dead spots, so the peak torque is much higher than the torque implied by its overall power.

[REdiculous]

Regular bike chain is pretty tough...I've got some old rusty chain on my trailer and it works just fine. I'll probably have to replace the freewheel before the chain now that I think about it.

[chuck]

REdiculous,

I just read your post on your build. Love it. I have never been the spit and polish kind of guy, like the mechanics, not the bling. Interesting. When I was a kid, I perused the neighborhood, scavenging parts, nailing and welding things together, used old motors and pulleys, made minibikes and go karts. All were fun, none lasted to long.

Unfortunately, I had to go to college and study. Parental pressure, I did not want to go. I am more of a hands on guy, would rather be in the shop than in the office. As a physics major I had to take a few injure-neering classes too. I have spent a lot of time the last 30 years since college working with power transmission design.

There are fundementals to good power transmission design that jawnn does not know yet. I know that jawnn is considering an etek type motor. That is a very powerful motor, hooked up to the correct batteries and the final gear ratio jawnn his considering would render bicycle chain useless in a very short time. I have got to run, I'll continue with good transmission design when I get back.

chuck

[chuck]

What is power transmission design?

I have used several primary reductions on my bike since the original version.

This one will handle 15 hp. 11/16th gates belt, 4" driven, 9" secondary, expected life, well over 20,000 hours

014.JPG (109.09 KiB) Viewed 474 times

015.JPG (65.05 KiB) Viewed 474 times

016.JPG (64.62 KiB) Viewed 474 times

The primary drive on the bike now is the one on the right, this is also the most efficient drive pictured, gates 3vx belt, 3.15" primary, 8" secondary. Expected life at its rated power of about 4.46 hp is 20,000 hours. Since I run about 1.6 hp thru it, It should last in excess of 400,000 miles, conservative estimate.

017.JPG (69.77 KiB) Viewed 474 times

I will re-edit this post, giving the actual efficiencies of each drive shown,

chuck

[jawnn]

Well I know this guy that builds these big trikes and claims that this is the only motor to use because he doesn't have to think about it. But then he says that the hub motors are even better....well I just keep thinking that I should use a leagal motor (that will require gears), even if the cops are not checking, and may not know what they are looking at.

He uses this on the tandom trike : http://thunderstruck-ev.com/etek_curve.htm
and a hub motor on the sinle person trike http://wildnaturesolutions.com/rockettrike.html

And my trike can't use a hub motor, so I must use some thing like a gear motor or make my own gears.
http://commutercycling.blogspot.com/200 ... guide.html

SO HOW DO I FIND A MOTOR THAT WILL WORK? a motor that will produce 1.2hp at around 95rpm? (and still be able to move faster on less steep hills) But is there a manufacturer that has charts for their motors?

I get vertualy no time on the internet, so I have to take this home to read it and come back in a few days bewildered as usual.

[amberwolf]

And my trike can't use a hub motor, so I must use some thing like a gear motor or make my own gears.
http://commutercycling.blogspot.com/200 ... guide.html

If that is your trike, I see no obvious reason it couldn't use a hub motor, at least in front.

SO HOW DO I FIND A MOTOR THAT WILL WORK? a motor that will produce 1.2hp at around 95rpm? (and still be able to move faster on less steep hills)

I use a brushed powerchair motor on CrazyBike2 to drive my regular bike drivetrain. It is nominally a 650w-ish motor (a bit under 1HP), at 24V. Running it at 36V, with the load I have on it, takes 15A-ish if I'm pedalling and cruising slowish, around 550W constant, or roughly half of what you need. It takes a lot more, in the 1.5 HP range with a heavy cargo load and faster speeds, or less pedalling; gets hot doing that. I'm sure with forced-air cooling, I could run it at more than 1.3HP for extended periods, perhaps constantly.

The nice thing is that at 24V it's meant to output about 120RPM from it's gearbox, and so even at 36V it doesn't take much reduction to get that to max of 90-ish at my drivetrain input to match pedalling speeds.

[chuck]

Jawnn,

I am a little confused too.

Read this again.
viewtopic.php?f=2&t=13418&start=0

What I need to know in order to answer your questions.

What is this trike to be used for?
What is the desired top speed of the trike?
What is the total distance you require this trike to travel?
What is the net change in elevation?
Do you have a picture of the trike you are interested in converting?

If you can answer the above questions I won't be confused anymore and I will be able to properly answer your questions
Is there a simple torque formula? No there is not. Is the mathematics difficult. No, I have made the calculations here using the math one should know by the 8th grade.

The concepts of Force, Energy and Power can be more difficult to understand. One needs to understand these three before the concept of torque.

Torque is a radial measure of force. It requires in its calculations the concept of pi and a high school level of mathematics of trigonometry to apply. Torque can be a monster, it is properly handled using college mathematics called calculas. In a static state torque is applied using algebra. Your trike is in motion which requires calculas to determine torque values.

Jawnn, answer the 5 questions from above with as much information as possible. Then we can proceed with answering your questions.

Respectfully,

chuck

[jawnn]

What is this trike to be used for? running around town with too much weight on the rear wheels, up steep hills that are wet most of the time.
What is the desired top speed of the trike? maybe 5mph on the hills.... or more...under 20 on the flats.

What is the total distance you require this trike to travel? maybe 30 miles.

What is the net change in elevation? the tallest hill, with a small amount of 16% is maybe about 200 ft

Do you have a picture of the trike you are interested in converting? its the same trike....there is vertualy no room except behind the seat for a motor. and it will be tight. the hub motor thing will not work...... so many people think it will and if I lived on flat land it could.

all I realy need is a big motor and a ratchiting free wheel for the axle that is I think 7/8th inch with a .5" key ... I may have to make one with a timeing belt sheave.