Climbing hills with as little energy as possible.

jawnn

jawnn

100 W
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Sep 3, 2009
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I have been talking to people in town and they all approach this problem from the desire for speed. Obviously I am going to have to do the experiments my self. So now I need a grant to fund this wild idea: ‘how to climb a 16% grade with as much weight as 450 lbs with as little energy as possible’.

I think it’s just a matter of gearing a 24-volt motor down to 60 RPMs and tying it into the drive train. But every one wants me to use a bigger motor and bigger batteries to increase the range and power. Well maybe I could find some one to sponsor a contest, not that it would be a popular concept.

If any one has a realistic reason why this can’t be done I would be interested, but only if they understand that I am not looking for more than 2 or 3 mph.

What I realy need to know is what is the minamum rpms a hlf hp motor will do and still have at 'least' a quarter hp?
 
To climb with very high torque efficiently, I would start with high motor RPM's. If you are talking about a 26" mountain bike (MTB) I would also consider using a 24" rear wheel.

to get 60 wheel-RPM's on a steep grade, while having high motor-RPM's (3,000-RPM's?) you will need a significant gear-down (50:1 total range). I would also start with 48V unless you were using one of the high-kV RC motors (which can be quite small) They can provide very high RPM's at lower voltages.

There are several builds that have installed a free-wheeling crank with a double-sprocket. This allows the motor to drive the Bottom Bracket (BB) which is the pedal-axle. In this way the motor can also use the bikes rear-axle gears. Cyclone and Elation sell these type of kits, and many enthusiasts have upgraded certain parts to make them stronger and more powerful.

Many others are adding a large sprocket to the rear-wheel disc-brake flange to make a Left-Side-Drive (LSD). RC motors are available in small sizes that spin to very high RPM's, so there has been some recent work building one-stage and two-stage drives as a gear-down (in addition to the final drive chain to the wheel).

Both configurations will be found in the "non-hub" section.

You also may consider a NiCD battery pack. Lihium is very good but more expensive, LiPo will be the lightest, and of course the inexpensive Sealed Lead Acid (SLA) will be bulky and heavy. NiCD can also easily provide high discharge amps. Best of luck, and have fun...
 
Give me a big enough leaver, and I can move the world.


You will want that motor its self spinning as fast as it can, drop the spead by gearing for the most power and most efficancy.
the further a motor is off it's peak RPMs, the less efficently it's running and the hotter it will get.

It takes 1 horsepower (750 watts) to lift 1 ton 1 foot in 1 minute. Moving a 450 pound weight up a 16% grade at 3 mph can be converted to an equasion based off that information. It takes some Trig. Can't do that in my head just now, but TD posted a chart with various weights, speeds, and inclines and the energy needed for each a few months back.
 
A big lever lets a small force move the object. But laws of physics will rule that it will still take a minimum quantity of energy to get the specified weight to the specified height.

The long lever still helps, allowing the smaller motor to do it, possibly with less wasted energy in friction and heat.

Of course pedaling more, like you do when you slow down really changes the ammount of energy taken from the battery. So doing that will get you up the hill with less used from the battery. I do this all the time when I need to extend range. The slower I ride, the larger the porportion of the total that is coming from pedaling is. Then you lose less from wind resistance too, and range gets longer still.

On my 5304 hill climber, the slowest I can ride it is about 5 mph, there is no slower throttle setting. A gearmotor though, might be able to go slower, if you have a trottle with fine enough low settings. Mine is sort of, off- --- and then 5 mph. So something other than a direct drive hubmotor would be needed to do slower gearing. On my pedaling MTB, I can ride as slow as 3 mph, but have no gears lower than that. 22 front 34 rear I think on that gear. Pretty hard to balance under 3 mph too.
 
I'm not sure you need a grant to learn basic mechanics and motor theory... The only thing that really matters is maximising the total efficiency of your system to climb the hill at the speed you choose. The energy used won't be greatly affected by the speed chosen (within reason).
 
Miles said:
I'm not sure you need a grant to learn basic mechanics and motor theory... The only thing that really matters is maximising the total efficiency of your system to climb the hill at the speed you choose. The energy used won't be greatly affected by the speed chosen (within reason).
Click to expand...

True. The baseline is going to be the weight you're lifting and you can't get under that (energy required = mass*height*gravitational_acceleration. This is also formally called potential energy. Given a hill of some height, your best bet is to lose some weight.), and any energy required after that is the energy required to push wind out of the way, overcome drive-train losses, feed the heat-producing motor, etc. Since the energy required to push wind out of the way is a function of speed, slower speeds and higher total system efficiency will allow one to get close to the minimum amount of energy required.

For maximizing drive-train efficiency, I think you're probably looking at as high an RPM as practical in a direct drive configuration and geared for "hill climbing" - most direct drive hubs suck for this purpose probably because of their low RPMs relative to their power outputs and the limited amount of practical gearing ratios, so a geared hub and and/or an external motor like an extremely powerful lightweight RC motor are common options. I usually find the hill-climbing "gears" by finding the gear ratio that corresponds to maximizing speed in my simulator (It optimizes it for me), and play with gear ratios higher than that that reduce lower heat and reduce the speed to something acceptable. Also, higher voltages (within reason) will be relatively more efficient, assuming the motor is geared down correspondingly.

(The difference in the energy needed to go 3 mph versus 10 mph isn't really significant. Actually, it might actually take more energy to go 2-3 mph because you may need greater reduction stages which entails increased drive-train losses and that may not offset the increase in air resistance with 10 mph.)
 
To go slower than 5 mph needs gears. But I ride at 5 mph up hills on DD motor all the time, on very little energy since I'm using the lowest possible throttle setting. To haul a lot of weight though would take more energy, that minimum discussed above. You may, however run into motor heating issues if the motor chosen doesn't have air cooling, so chain drive, or stokemonkey type setups might be best. It just depends on how long the hill is, whether motor heat becomes an issue. My fusin, similar to a bafang hubmotor gets very hot in just a couple miles when climbing at 13%.
 
At a velocity of 3 mph you will need about .6 hp.

Weight = 450 lbs
slope = 16/100, using a^2 + b^2 = c^2 , skip the trig, use 16/101.27
velocity = 3 mph or 4.4 ft/sec
frontal area about 7.5 square feet

The force of drag is 1/2 (air density)(coefficient of drag)(Frontal area)(velocity^2)
Fd = 1/2(.00273)(.9)( 7.5)(4.4^2) = .18 lbs

The force of rolling on my bike is about 3 lbs using maxxis hookworm tires at 40 psi with about 450 lbs of weight
Fr = 3 lbs

The force of the hill is weight * corrected slope or 450 * 16/101.27
Fh = 71 lbs

Add the 3 forces to find the total force
Total force = 74.18 lbs

To find the power required at the pavement multiply by the velocity
74.18 lbs * 4.4 ft/sec = 326.4 ftlbs/s

1 horsepower = 550 ftlbs/sec

326.4/550 = .6 horsepower

To find the gear ratio.

I have a scott 24 volt motor, 1 hp at 3000 rpm peak effiency.

Use a 26 inch mountain bike wheel. Its diameter is 26 inches/12 inches,,,to get feet,,, = 2.167 feet
Its circumference is 2.167 * pi = 6.8 feet

at 4.4 feet/sec this wheel must spin at 4.4/6.8 revolutions per second or .646 rps
convert this to rpm by multiplying by 60
Wheel rpm = .646 * 60 = to about 38.8 rpm

The reduction ratio is the motor rpm / the wheel rpm or 3000/38.8
Reduction ratio = 77.36 to one

For a 2 stage reduction take the square root of the reduction ratio or about 8.8 reduction ratio per stage
3/8ths pitch or number 35 chain will handle .6 hp with a 10 tooth sprocket at fairly low rpms, not ideal, but about the only thing available. Sprockets of 96 tooth are commonly available, use the chain for the wheel reduction.

96/10 = 9.6 ratio for the wheel reduction, lets find the motor stage reduction

77.36/9.6 = about 8 to 1

A 3v v-belt will handle this power at above 95% efficiency. Do not use a 3L belt, they both fit on the same size sheave, the L stands for light duty. The v stands for industrial. Lets try a 12 inch sheave to get that 8 to 1 ratio. 12/8 equals a motor pulley of 1.5 inches, perfectly fine size for a 3v "premium" called a 3vx belt.

Now, we are real close to a final ratio of 77.36 to one

V-belts have a pitch ratio, subtract .05" from each sheave to get the actual reduction. 11.95/1.45 = 8.24 ratio on the motor.
Divide the 8.24 ratio into the total ratio of 77.36 to get the final ratio of the rear drive. 77.36/8.24 = 9.386
ok, I am pretty sure one can find a #35 pitch chain sprocket with 96 teeth at a reasonable price. To find the jack shaft sprocket, divide the wheel sprocket by the remaining ratio, ie 96/9.386 = about a 10 tooth sprocket.

The final ratio is (96/10) * (11.95/1.45) = about 79 to 1..

(79 - 77.36)/77.36 = about 2 % off, reduce your speed of 4.4 by 2% for peak efficiency,

Don't ask me to calculate the efficiencies of these drives, but, the chain will probably be about 90% efficient, the belt about 95%.

Take the horsepower of .6 and divide by the power transmission efficiency of about 85% or .85.

.6/.85 = to about .7 hp the motor needs to put out. The motor and controller as a combination are about 85% efficient.
.7/.85 = about .83 hp. This is what the battery needs to supply. Convert hp to watts. 1 hp = 746 watts

The battery needs to supply .83 hp * 746 watts = 620 watts

For a 24 volt system the amps are 620 watts/24 volts = to about 26 amps

I use agm batteries that have a reserve capacity of 135 minutes at 25 amps. I use a 24 volt system with 68 ah batteries.

My reserve capacity in hours is 135/60 = 2.25 hours.

At 3 mph * 2.25 hours I will travel 6.75 miles up your hill. The scott motor will be warm, not smoking hot, at this output.

chuck
 
chuck said:
At a velocity of 3 mph you will need about .6 hp.

Weight = 450 lbs
slope = 16/100, using a^2 + b^2 = c^2 , skip the trig, use 16/101.27
velocity = 3 mph or 4.4 ft/sec
frontal area about 7.5 square feet

The force of drag is 1/2 (air density)(coefficient of drag)(Frontal area)(velocity^2)
Fd = 1/2(.00273)(.9)( 7.5)(4.4^2) = .18 lbs

The force of rolling on my bike is about 3 lbs using maxxis hookworm tires at 40 psi with about 450 lbs of weight
Fr = 3 lbs

The force of the hill is weight * corrected slope or 450 * 16/101.27
Fh = 71 lbs

Add the 3 forces to find the total force
Total force = 74.18 lbs

To find the power required at the pavement multiply by the velocity
74.18 lbs * 4.4 ft/sec = 326.4 ftlbs/s

1 horsepower = 550 ftlbs/sec

326.4/550 = .6 horsepower

To find the gear ratio.

I have a scott 24 volt motor, 1 hp at 3000 rpm peak effiency.

Use a 26 inch mountain bike wheel. Its diameter is 26 inches/12 inches,,,to get feet,,, = 2.167 feet
Its circumference is 2.167 * pi = 6.8 feet

at 4.4 feet/sec this wheel must spin at 4.4/6.8 revolutions per second or .646 rps
convert this to rpm by multiplying by 60
Wheel rpm = .646 * 60 = to about 38.8 rpm

The reduction ratio is the motor rpm / the wheel rpm or 3000/38.8
Reduction ratio = 77.36 to one

For a 2 stage reduction take the square root of the reduction ratio or about 8.8 reduction ratio per stage
3/8ths pitch or number 35 chain will handle .6 hp with a 10 tooth sprocket at fairly low rpms, not ideal, but about the only thing available. Sprockets of 96 tooth are commonly available, use the chain for the wheel reduction.

96/10 = 9.6 ratio for the wheel reduction, lets find the motor stage reduction

77.36/9.6 = about 8 to 1

A 3v v-belt will handle this power at above 95% efficiency. Do not use a 3L belt, they both fit on the same size sheave, the L stands for light duty. The v stands for industrial. Lets try a 12 inch sheave to get that 8 to 1 ratio. 12/8 equals a motor pulley of 1.5 inches, perfectly fine size for a 3v "premium" called a 3vx belt.

Now, we are real close to a final ratio of 77.36 to one

V-belts have a pitch ratio, subtract .05" from each sheave to get the actual reduction. 11.95/1.45 = 8.24 ratio on the motor.
Divide the 8.24 ratio into the total ratio of 77.36 to get the final ratio of the rear drive. 77.36/8.24 = 9.386
ok, I am pretty sure one can find a #35 pitch chain sprocket with 96 teeth at a reasonable price. To find the jack shaft sprocket, divide the wheel sprocket by the remaining ratio, ie 96/9.386 = about a 10 tooth sprocket.

The final ratio is (96/10) * (11.95/1.45) = about 79 to 1..

(79 - 77.36)/77.36 = about 2 % off, reduce your speed of 4.4 by 2% for peak efficiency,

Don't ask me to calculate the efficiencies of these drives, but, the chain will probably be about 90% efficient, the belt about 95%.

Take the horsepower of .6 and divide by the power transmission efficiency of about 85% or .85.

.6/.85 = to about .7 hp the motor needs to put out. The motor and controller as a combination are about 85% efficient.
.7/.85 = about .83 hp. This is what the battery needs to supply. Convert hp to watts. 1 hp = 746 watts

The battery needs to supply .83 hp * 746 watts = 620 watts

For a 24 volt system the amps are 620 watts/24 volts = to about 26 amps

I use agm batteries that have a reserve capacity of 135 minutes at 25 amps. I use a 24 volt system with 68 ah batteries.

My reserve capacity in hours is 135/60 = 2.25 hours.

At 3 mph * 2.25 hours I will travel 6.75 miles up your hill. The scott motor will be warm, not smoking hot, at this output.

chuck
Click to expand...

Lot of free time?
 
The best advice so far is to start with a high RPM and keep it there.

Stop thinking speed, this is a trike with trailer and plenty cargo.

60 rpm’s will be the crank speed (for my legs) Possibly 80 with muscle input.

My lowest gear is a 1 to 1.88 ratio (18 sprockets front/ by 34 rear). That makes my 20” tire turn at about 32 rpm’s or 1.89mph? (I did not use a formula for this, just brain storming, so I don’t know that it is correct)

The next gear is 28 sprockets front/ 34 rear = 3 mph

Well maybe a bit slower even is the tires are 85psi, but if I use my legs I may need a speedometer.
.
Will a 500w 24v motor push 400lbs plus the weight of the power system, batteries and all, up the 16% grade at 1.75 mph???

This is not a long hill but there are other hills to deal with.
 
You may do it that slow on 200 watts. You're in an area where you'll have to do your own experimenting to see what works though. A stokemonkey setup on a trike or a cyclone might do it with low enough gearing.

If you think about it, dump trucks haul huge loads up hills with not that big of engines. But they have at least 8 gears, and the low ones are incredibly low.

The total energy used is set in stone, but the size of the engine providing it isn't.
 
jawnn said:
The best advice so far is to start with a high RPM and keep it there.

Stop thinking speed, this is a trike with trailer and plenty cargo.
Click to expand...

The best advice is to keep MOTOR RPM high and gear it down so that you get LOW WHEEL RPM = LOW SPEED. Hard to understand?

This has all the benefits as explained above, the least of which is high efficiency which is what you'll need for minimizing energy usage.
 
Well I am compleetly lost...


Will a 48-volt motor have a lower peak efficiency rpm than a 24-volt at the same 500 watt (or possibly less)???

Maybe I should just gear down to 80 rpm’s and enter the drive train between the crank and the rear sprockets. In fact I could use an even higher rpm (how musch higher is beyond my brain power) if I gear it down at the entry point, but remember that I want to power this with my legs only as much as possible. That’s why I want as small a power system as possible.

Seems to me that the gearing down of the motor will be the hardest part.
 
Depends on the approach, a stokemonkey setup of a gearmotor would be really low geared.

Stokemonkey is a hubmotor, usually direct drive, that is mounted in the middle of the frame instead of in the wheel. Then the motor has a sprocket to chain drive the rear wheel. Using a motor with internal gearing instead should result in super low gearing, allowing an efficient 250 watts to spin the motor fast, and the wheels very slow with incredible tourque.

A regular cyclone set up would be really low geared if you put an intermediary gear in between. My trike had such a gear setup, with the pedals driving a sprocket, that drove another chain to the sprocket on the axle. Making the last sprocket on the axle bigger would have lowered the ratio by a lot.

Another approach would be to lengthen the front forks, so that a 20 inch wheel could be mounted, and then put a gearmotor with 20" rim in it. The forks from a folding bike might be perfect, or longer suspension forks might be the ticket. A gearmotor in a 20" wheel would be a torque monster.

But seriously, a 16% hill is gas engine territory.
 
Yep! Lots 'o torque from a 20" wheel gear motor. All I ever ride. BUT, you run out of steam at 10-12 mph and then you're on your own pedaling. I have a low recumbent but even busting my old AS* I cant get more than 16 to 17 mph except downhill. Now on 48 volts............or 60.............. :twisted:
otherDoc
 
Oh yeah! Current is quite low, usually about 6-10 amps even on a hill, on level sometimes 4-6 on the Whattmeter. Gears rule!
otherDoc
 
Yup the more I think about this one, a planetary gearmotor in a small rim would do the trick nicely with the least hassle. If the trike has a big front wheel, just replace the forks with longer ones and use either disk brakes or get the rim brake mounts welded on lower for a 20" wheel. Torque monster but slow. But it's a cargo trike I think, so slow is fine.
 
Could some one tell me what I am doing wrong? I checked this on two diferent calculators….it must be human error. I know for a fact that I am not moving at 6.7 mph people walk past me.


34 sprockets divided by 18 on the crank = 1.8888 ratio

x 60 rpm’s at the crank = 113.328 tire speed

x 62.8” circumference = 6799.68 (or 7117.332?)

Divided by 12 inches =566.64 (or593.111?) ft per minute

x 60minutes = 33998.4 (or35586.66?) ft per hour

Divided by 5280 = 1.55 mph or (6.73?)
 
I need more info about hub motors...like what is the differance between the stoke monky and te Heinzman?

I presume that I will just have to experiment t see exactly what they will do for weight. Know any one that would fund such experiments?

I would mount one under the seat and chain it to the crank... the front wheel is set at 60 degrees and I think there would be too much wheel flop and not enough traction on wet steep hills.

This is a Sun EZ3 USX trike.
 
jawnn said:
I need more info about hub motors...like what is the differance between the stoke monky and te Heinzman?

I presume that I will just have to experiment t see exactly what they will do for weight. Know any one that would fund such experiments?

I would mount one under the seat and chain it to the crank... the front wheel is set at 60 degrees and I think there would be too much wheel flop and not enough traction on wet steep hills.

This is a Sun EZ3 USX trike.
Click to expand...

You've got the right idea about the motor in the front. With that trike, all the weight over the back wheels means the front would slip too easy trying to climb.

Hub motors are just that, Motors that replace the hub. The spokes lace to the outside of the motor and run the wheel directly.
there are two types. gearless, and geared.
Gearless work like a ceiling fan. there are no gears, and only 1 moving part.they are silent, and highly efficent at cruising speed but low on torque.
Geared hub motors are just that, geared. A small, high RPM motor turns through a set of internal planitary gears to turn the outside of the motor. They are generaly smaller, lighter, and have better climbing torque and acceleration than a gearless hub motor, but are noisier, less efficent at full speed, and have less mass to absorb and disapate heat.

The Stoke monkey is a gearless hub motor, removed from the wheel and running through a chain. It has all of the disadvantages of the hub motor, like being large, heavy, and low on torque, combined with the disadvantages of a chain drive, like more moving parts, noise, alignment issues, and loss of efficancy through the driveline.

The Hiezman is a geared hub motor. Its an older design, and not brushless, but they were so well made that they rival some of the newer generation motors.

But most of this is moot for you. There aren't any production motors that can be run on the type of axle that trike uses. About your only option is going to be some form of chain drive motor
 
It would take a bit of work but...........

http://tncscooters.com/product.php?sku=106124

otherDoc
 
jawnn said:
I know for a fact that I am not moving at 6.7 mph people walk past me.
Click to expand...
Math is my worst subject, but here goes...

18 / 34 = .53
crank : sprocket = 1 : .53

60 rpm’s at the crank * (.53) = X (wheel rpm)
60 (.53) = 31.76 rpm

62.8” circumference * rpm = ipm
31.76 * 62.8 = 1994.82 ipm

Divided by 12 inches = ft per minute
1994.82 / 12 = 166.235 fpm

x 60minutes = ft per hour
166.235 x 60 = 9974.117 fph

Divided by 5280 = mph
9974.117 / 5280 = 1.889 mph


This 1000W motor and gearbox are cheap and about as quiet as a hubmotor . A sprocket could easily be mounted on the output shaft (440rpm), then connect to a freewheel on the rear axle:
file.php

http://endless-sphere.com/forums/viewtopic.php?f=28&t=13622&p=202019#p202019
 
This is a Sun EZ3 USX trike.
Click to expand...
Hi Jawnn. I have the same trike and a 15% grade on the road to my house, plus 20% for a very short distance on my own driveway.

I understand you are not interested in speed and you also want to keep the motor weight down, so I am just going to share some of my experiments and give my thoughts on what I would do.

First thought, I would not motorize that trike through it's drive train. Only the right wheel is driven and with no trailer, no motor, and no extra weight, I can not get started on a 20% grade. When you give it enough power to move the front wheel just slides to the left. Even when moving up a steep hill you have to be careful not to start "crab walking" the front wheel.

When I first purchased the trike I had already set up a bike with three hub motors in 26" wheels. One on the front of the bike and the other two on a pusher trailer. These were all BD36's at 36V. I set up the trike the same way, except the BD36's were all in 20" wheels. Later I removed the hub motor from the front wheel and upped the trailer motors to 48V. The hill climbing ability remained about the same. These hub motor/wheels weigh about 15#'s each.

I built a new trailer for this trike using two scooter motors. These motor/wheels weigh about 30 pounds each, they top out just under 30 MPH, and have lots of lower speed torque for hill climbing.

Last fall I set up a BOB trailer with a Bafang laced into a 16" wheel. I purchased this from JohnRobHolmes of this forum. At my request, he used the standard front Bafang manufactured for use in a 26" wheel. This resulted in a slow speed high torque motor which is virtually unstoppable on my hills. Even though it's top speed is under 15 MPH it will keep close to 12 MPH on the hill. It is also running at 48V. These little motors only weigh about 7 1/2 pounds. To be Continued...thread issue?
 
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