Wattage vs Torque/Pulling Power.

Hi,

I have been mulling over getting a rear hub motor for my MTB.

Given that I am already equipped with a front hub with 700 watt rating, I found myself asking just what do I want the rear hub to do.

The answer: an auxiliary, workhorse wheel designed to aid during severe uphill treks and on flat runs with a 50l backpack filled with scrap metal. In other words- donkey work.

How then do we distinguish between watts and torque?

Does a 1000w motor necessarily have more torque than a 700 watt motor?

Is 700 Watts of Cammy power incapable of performing more work than 500w of Golden Motor?

Horsepower is often measured in Kilowatts, and we know there is a difference between Torque and Horsepower.

Or does it all depend on the voltage of the motor combined with the wattage rating of the motor?

Does a 48v 10Ah Battery +500w Hub perform more or less work than a 36v 20Ah battery+ 700w Hub, with all things being considered equal?

Thanks for your considered opinions.

ebikes.ca motor simulator

And it's a new version that includes motor inductance too now!

Have fun playing with it, and there's also lots of well structured info below the simulator.

All manufacturers want their products to look good compared to the competition, so the labels are sometimes a little optimistic. A 120V motor can be small, and can be wound for any RPM you want. But getting the same watts from a lower voltage motor means you need more amps, and that means more heat.

Even if a motor is rated for a continuous 500W @36V, you can temporarily pump a higher voltage and/or amps through it. When you do that, the motor/controller will be absorbing heat faster than it can shed it, and they will slowly get hotter and hotter. If its just for a short hill, once you reach the top, the motor can start cooling back down to normal running temps.

Larger motors have more mass to absorb and shed more continuous-heat/temporary-excess-heat. A larger diameter motor will automatically have more leverage and torque per the same watts put into it.

If you are willing to sacrifice top-speed (either temporarily with a transmission shift, or all the time) gearing down a 500W motor, or driving a smaller diameter wheel will give you more hill-climbing/cargo torque. So...

A 500W motor driving speed sprockets on a large diameter wheel will be fast on the flats, but bog down easily with almost no torque.

A 500W motor driving low-gear sprockets on a smaller wheel, will be slow, but will pull heavy loads well.

A 500W motor driving a multi-speed transmission on a medium diameter wheel can choose either as desired.

Getting those 500W from high-amps/low-volts means lots of heat, and it will need thick wires and a battery with a high-C rate. It would have slow acceleration to get to its top speed. If the 700W hub is physically bigger, it might be able to shed more heat under load, and then you should start with the highest volts you can afford, because for donkey work its all about the heat ("severe uphill treks...50l backpack filled with scrap metal").

If you are going to beat your cargo-bike like a rented mule, and are set on a hub instead of a non-hub, get a Clyte 530X, or if thats too expensive for your budget, maybe a 9C, and hit it with the highest volts you can afford. Choose the tire diameter first (24" has more torque than 26") system voltage next, then choose a motor winding that provides the slowest top speed (at those volts) that you can be happy with in order to get the maximum torque from whatever watts you're feeding it. (more amps can be added later, or temporarily limited if getting hot. Changing volts is a whole system change, controller, battery, motor winding, etc)

I'm going to assume you are looking for tourqe, and power. The two do not have to go together. for instance...

My fusin 350 watt motor has great tourqe. You can really feel it. But alas, with only 350 watts of controller on it, it's not that impressive on a hill. You can still stall it fairly easy. The internal gears give it the mechanical advantage, and give it enough power and it will really pull! But then you have the effect spinningmagnets talks about where you can melt down stuff if you push that hard too long. In general, gearmotors shed the heat slower than a dd hubmotor. So slow in fact, that you can have the motor hot as hell inside, and the outer case may still feel cool.

Another way to improve tourqe of a motor mechanically is to make a direct drive motor in a larger diameter. This gives the magnets a longer lever to pull on, improving tourqe. The larger mass absorbs a bit more heat, and the larger cover sheds it a bit faster. All good things, examples of this are the 9continent and 530x clytes.

does a 750 watt motor have less tourqe than a 1000 watt motor? yes and no. depends on many variables. One guy may call his motor 750 watt, because the motor, at full speed on the flat, pulls 750 watts, and besides, he wants to sell a US, street legal bike. The same dang kit may be called a 1000 watt by another guy, because, in fact, the setup pulls 1000 watts going uphill.

Another example. same motor, different controllers. One is 36v 20 amps, the other 36v 35 amps. The 35 amp one is going to have more tourqe, IF, it is used with a battery capable of the 35 amps.

Another example. Same motor, same controller, different voltage. The same motor will have more tourqe when run at 48v than it did at 36v.

In general, all the mid size direct drive motors handle a wattage range from 500-1500 watts pretty well. Some may have skinny phase wires for 1500 watts, but the innards are very similar. This would be golden motors, aotema(wilderness energy), clyte 400 series, 9 continent, etc. In this list the 9c has the tourqe advantage since it is a large diameter hub.

You might want to consider a second motor on a push trailer. Easy to remove when you don't need it, and lots of room for more battery to run it.

This is an interesting subject to me as it involves motor technology and hill climbing ability. The last two comments were excellent and I hope some other experts will contribute. With ebikes there are always variables. In regards to the larger diameter motors having more torque, that's logical if all other variables are equal. For example, the Aotema with a smaller diameter than the 9C, has very similar torque due to larger magnets and a metal ring surrounding the magnets (verses Al) which magnifies the field. This compensates for the smaller diameter and is a more advanced design in my humble opinion. (full disclosure: my company sells the Aotema motor)

When designing a system, I try to stick to 36V for cost reasons and common components. Most production ebikes are 15 amps which is good for 18 mph or pedal assist, and very minor hills. The next step, and starting place for people here, is 20 amps and 20mph and depending on geared or DD motor, medium hills up to 5- 9 % grade. For heavy loads and 10% - 12% grades, jump to 35A controller and a good battery back like a LiFePO4 15AH or 20AH. This is still a reasonably priced system. If that doesn't cut it, then you can go to 48V which provides the same power at a lower current and a higher total power. But, you have to be careful here because the higher voltage (and power) might be wasted in higher speed which you don't want. So, you have to get a motor that is wired for the max speed you will want (at 48V). Then you can go up the current scale again as needed. Now you start reaching the max power rating of the reasonably priced (and weight) motors. Note that once you opt for this setup, you are limited by always having to use 48V unless you want to go slow. Another option if you don't want one huge, heavy motor like the 5300 series is a dual motor setup. Great for hills, but that is the subject for another thread.

HTB_Terry said:

. If that doesn't cut it, then you can go to 48V which provides the same power at a lower current and a higher total power. But, you have to be careful here because the higher voltage (and power) might be wasted in higher speed which you don't want. So, you have to get a motor that is wired for the max speed you will want (at 48V). Then you can go up the current scale again as needed. Now you start reaching the max power rating of the reasonably priced (and weight) motors. Note that once you opt for this setup, you are limited by always having to use 48V unless you want to go slow. Another option if you don't want one huge, heavy motor like the 5300 series is a dual motor setup. Great for hills, but that is the subject for another thread.

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48V which provides the same power at a lower current and a higher total power

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I'm calling you on this because you're wrong! Upping the voltage draws the same current but creates more wattage due to the higher voltage :lol:

you have to be careful here because the higher voltage (and power) might be wasted in higher speed which you don't want.

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Engineering in design deficientcy's is the whole problem with E-bike retailers! Selling crappy shit is just
Limit the bike when you sell it through software ex. Cycle Analist... www.ebikes.ca. as for your dual hub bike :lol: :|

Thanks for calling me an expert Terry, but I'm still pretty dumb with electronics. But I have experience riding motors to death which beats theory at times.

I think you misinterpreted one of Terry's comments, Affliction. Terry was talking higher voltage, but lower current, not higher voltage same current. Higher voltage same current would be more watts, as you point out. Current might be limited by a lower current controller, or CA, or a battery bms, etc. With the same controller, current would not be less I'd think, as you say.

As for the tourqe of the Aotema vs 9c, the 9c wins the tourqe contest and the hill speed contest in my tests. This was the HTB kit and it's controller head to head vs the E-BikeKit and it's controller. Some of the difference could be controller, but the 9c has a slower top speed so I'm thinking the windings are different enough for it to be not so equal. Different type motors will be different.

I wouldn't say the 9c kit is better than the aotema kit though by a long shot. Just different. The HTB kit sesnsorless controller kicks ass, since no hall wires kicks ass.

The HTB kit is faster at the same voltage on the flat, and is fast enough for me on a hill. In limited tests I've done, the HTB motor did not seem to get hot faster, or end up hotter climbing the 7% test hill than the 9c. The speed difference would only matter if your ride was up some really really long hills that might melt down either motor. But the faster speed on the rest of the ride will get you there sooner with the Aotema. There is, of course, a faster winding 9c, but I haven't tested that one so I'll say nothing about it. The E-BikeKit is aimed at 20 mph at 36v which is the legal limit in most of the US. In my state though, there is no ebike law, so I'm a moped and in this state legal to 25 mph. That makes me legal on the Aotema at 24 mph. Gotta carry a valid drivers licence though.

Eventually I'll get through the running stock portion of the review on the 9c and start comparing the motors on the sensorless controller for a more fair test of tourqe, range, speed etc on the same sensorless controller. Next summer we'll see how the 9c stacks up for taking the heat too. I spent all last summer trying to melt my aotema and couldn't do it on my normal 15 miles uphill ride home. It was kinda cool though, none of the rides home was over 105F ambient temp.

Judging by the comments of a previous poster who first "called me out" then proceeded to "correct" my comments by basically restating them, there is a lot of confusion regarding this subject. I think it would be helpful at this point to review some basic electronics. Not everyone on here is an electronics engineer with 20 years experience. First, the formula for power is P=V x I power = voltage times current

P = Power, measured in watts (W)
V (or E) = Voltage, measured in volts (V)
I = Current, measured in amps (A)

Voltage and current are directly proportional to the power in watts, so raising voltage, raises power. So you could have the same power level with different values of current and voltage. For example 36V and 20A = 720 watts, and 48V and 15A = 720 watts. This was one of the points I was making, that with a 48V system, you can obtain the same power with lower current. The other point I was making (I combined them in one sentence) was that the 48V system gives you a higher total power assuming the max current is the same. So with 20A limit the 36V system gives you 720W and the 48V system gives you 960W. These are fundamental principles of electronics and can not be disputed.

This basic electronic knowledge should be used as a foundation on which to base a more highly technical discussion of motor design and power requirements. So, relating this to ebikes and motors, one must detgermine how much power is required for a given situation and how to achieve that power. From the results of Dogman's and other's testing, one can get a rough estimate of what is required. Let's say it takes 500-600 watts to get up a medium hill with some pedaling. In that case a 36V 20A system should do the job. For steeper hills and or heavier loads around 750 to 1000 watts is required. For very steep hills, around 1500 watts is needed. Of course there are always variables, I'm just giving some rough numbers to make a point. Lets say you figure you need 1000 watts. So at 36V you would need about 28 amps. That's beyond the common 20A controller so you would need a high power controller and a battery pack able to sustain that current, still doable with 36V but with an expensive battery. Now suppose you determine you need 1500 watts. At 36V you would need 42A, a huge current, double the typical ebike. The motor most likely would not be operating very efficiently at these values. At this point it would make sense to upgrade to 48V where the current requirement is a more manageable 31A.

Going back to the original poster's questions, and where my interest lies, is what motor running at what voltage is the most efficient for a given situation. What about torque? Given two identical motors, one wired for 36V/20mph and one for 48V/20mph which one is more efficient? When to use one over the other? Under what conditions does a geared motor have more torque than a DD motor? At what power level does a DD motor have more torque than a geared motor? What is the criteria for picking a particular setup for a given requirement?

Some things to think about and balance against each other:

1. Price of system, particularly the battery pack (48V is expensive)
2. Total power needed, not too little but don't wast money on power you don't need
3. Trade off some pedal power for cost?
4. Battery size and weight vs range.
5. Front vs Rear motor, front has good weight balance but rear better for steep hills.
6. 36V or 48V system, cost verses power requirement, motor efficiency
7. If choosing 48V system, get motor with correct winding to match desired speed. (don't waste power on excess speed)

I think the most important principle in all this is motor efficiency. You must get the required power to the wheel without wasting battery power and creating heat in the motor. Low efficiency = high heat and wasted power. The goal is to determine the motor (and voltage) that will operate the most efficiently in the specific situation that is required. For example, a particular hill with a given weight.

Anyway, that's my two cents. I think the original poster (and myself) would appreciate input from actual experts who will post intelligent comments and suggestions. It's great people get excited and feel compelled to post, but I hope this thread will consist of technical facts and test results rather than irrelevent comments that just further confuse people.

Voltage and current are directly proportional to the power in watts, so raising voltage, raises power. So you could have the same power level with different values of current and voltage. For example 36V and 20A = 720 watts, and 48V and 15A = 720 watts. This was one of the points I was making, that with a 48V system, you can obtain the same power with lower current. The other point I was making (I combined them in one sentence) was that the 48V system gives you a higher total power assuming the max current is the same. So with 20A limit the 36V system gives you 720W and the 48V system gives you 960W. These are fundamental principles of electronics and can not be disputed.

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I'm not disputing this at all, your other statement was not clear on this point. But I knew what you meant
On the sphere you have to explain things to death or new users of E-bikes can get confuzed.
I know you are a retailer and I took a crack at your 2, 250 watt bike but you are limited on what you can legally sell to the public.
Alot of people who buy their first legal ebike soon get boord of the limits. Increasing the voltage is the easiest way to get more pep out of their systems. Problem is that most cheap controllers can only handle up to 72 volts. A full charge 48 volt battery is right on this threshold. (full charge 48 fresh off the charger is almost 60 volts)
You kind of stated this but not clear enough. I take exception to ebike kits that are proprietary and can't be easilly modified. Controllers purposely installed for a lower amp limit is one of these things. Why not just sell a 36 volt battery instead? Still legal with the higer amp controller and then let the customer decide if they want it more powerfull down the road. Bionx is one of these company's; you can't do shit with their systems mind you installing a pl350 on a bike with a 250 motor is quite impressive
You keep talking about efficentcy as it relates to voltage and motor speed. Don't confuze the subject.... If you put 48 volt batteries on a 36 volt system and you do the same speed and watt limit as it was with 36 volts then there is no difference in efficentcy. What changes as the original starter of this thread was asking is you have more available wattage and thus more torque. You don't have to drive full throttle all the time!
I have a friend who is quite content with 36 volt lithium but when it comes to hauling his trailer with his 100+lb rotweiller then he uses 48 volts for the extra torque. It's not about speed!

Factoring torque is not so handy for addressing the OP's practical issue...

It will take X amount of power to do X work at X speed.

That will take a system that can sustain delivering X power at X rate for X duration, without damage.

The OP already reports 700W. Assuming that is a continuous rating, another 1200W or more (continuous rated) would be reasonable. Less power could be ok if the speed or duration are reduced.

Figures in the chart were derived from the now-defunct kreuzotter calculator, using an average rider/bike profile.

The Mighty Volt said:

Hi,
I have been mulling over getting a rear hub motor for my MTB.
Given that I am already equipped with a front hub with 700 watt rating, I found myself asking just what do I want the rear hub to do.
The answer: an auxiliary, workhorse wheel designed to aid during severe uphill treks and on flat runs with a 50l backpack filled with scrap metal. In other words- donkey work.

Click to expand...

The simple answer is, two motors of the same rating and controller will double your pulling power if your battery can handle it.
The rating of motors is not conformal. but if you take the rating at the voltage advertised with the kit then you get an idea.
36 volt at 500 watts translates to 667 watts at 48 volts. The amp rating of controllers is not set in stone either, I have had many 20 A controllers that draw more than 30 amps! I imagine your 700 watt rating is at 48 volts by convention on all the stuff coming from china.
So actually you have a 500 watt motor at 36 volts.
Now I have stated that most "classified" 20A controllers draw 30A, then the real issue is battery capacity and continuous and peak amp draw.
Lithium hates sustained peak loads unless you want to kill it. Now we have calculated 60A for two 20A controllers for use.
A good cheap battery for 60A+ usage is 12 amp/hr sla's. In normal riding and you are using both motors you can half the amp draw that one would do.
Now from my own experience on using different motors front and back.... Not worth it, too many wierd issues. Just get the same motor for the rear of your bike,

Okay, thank you all for your contribiutions!! I probably should have pointed out in advance that I have already got a 48v 20Ah Cammy_CC special lined up for the new hub, whatever that new hub is.

The Mighty Volt said:

Okay, thank you all for your contribiutions!! I probably should have pointed out in advance that I have already got a 48v 20Ah Cammy_CC special lined up for the new hub, whatever that new hub is.

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is that a battery? just drive both hubs with it if it;s 20ah
You know what!? I think Mighty Volt is frocking with us......just got that feeling. He seems to have knowledge on other posts but goes totally stupid again. I don't like posers! Volt is a poser troll and just ignore it.

Nah, my BS radar says TMV is legit. Regardless, the discussion is worthwhile.

Another 700W hub might not do the donkey-work.... The OP needs to pull up steep hills with an extra >100lbs of load.

We should assume moderate speeds and long enough duration to burn a small hubbie.

A 48V-20ah pack may not last long if the load is 2KW continuous.

A 1KW Cyclone kit is a no-brainer... the OP needs a tractor, not a cruiser.

Horsepower and Torque: A Practical Explanation

This may be the least understood relationships in motors. here is an attempt to explain it.

Force

Force is the pressure of one mass against another, and is one of the primary units in all of physics. In the metric system, force is calculated in "Newtons". Gravity is an easy example of a natural force and is written in the English system as "pounds". So we also use pounds as the basic unit of force.

Work

Work is defined as force over distance and is calculated as Work= Force * Distance. In other words, work is achieved when force causes an object to move. The force placed on the object and the distance it moves are calculated as the work done.

Power

Power was originally defined by the engineer James Watt as the amount of work that can be done in a certain amount of time. So its function is Power = Work / Time. for example lifting a 550lb weight a height of 1ft is 550 lb-ft of work. doing that amount of work per second is 1Hp. another example - lifting 1100lbs a height of 1/2 ft in 1 sec is still only 1HP. though i have lifted twice the weight i have only lifted it 1/2 of the distance in the same amount of time so it is the same amount of power.

Torque

Torque is defined as the force at any one point on the edge of a circle in the exact direction of the rotation multiplied by the radius (distance from the center). This comes from the calculus/geometry concept of a "tangent", a line which touches exactly one point of the edge of a circle.


In the metric system, force is calculated in newtons, and distance is in meters, so the standard torque unit is Newton-Meters or N-M. In the Standard/English system, force is calculated in pounds and distance in feet. So the torque unit is lb-ft, usually pronounced as "Foot-pounds" and sometimes written as "ft/lb".

Horsepower

Horsepower is a unit of power. It can be defined in many ways. In its basic sense, it's defined as work done in a straight line as described above under "Power". But when the work is not done in a straight line, it must be defined in a different way: torque. Torque is the measure of the rotational force produced at the edge of a wheel.

Horsepower = (Torque X RPM) / 5252.

Now although horsepower in this instance is defined by rotational forces, it is no different than straight-line horsepower. For instance, if you wrapped a rope around the circle and allowed the torque to pull the rope, the force on the rope would now be exactly as defined above. that 5252 number is a constant. it is derived from all of the conversions done to convert RPM to revolutions per second, converting torque to linear force and other conversions to get all of the units correct lumped together into a single number.

so now if i have 2 different motors. one a high turn count, low speed 9C motor matched to a 26" wheel and a low turn count, high speed 9C motor matched to 20" wheel. both motors are still only 500W and are connected to identical batteries and controllers. the low rpm motor will produce a certain amount of force to turn that 26" wheel a certain number of times in 1 second to propel the bike a certain distance.

the high speed motor will turn the 20" wheel a greater number of times in the same second. it can produce higher rpm but with less force. it would have to to make the smaller wheel travel the same distance as the 26" motor of the same power. same distance traveled for the same power input means they are the same power - 500W.

now of course if i fudge this by using a bigger controller and more amps and volts i can make my high rpm motor produce more power. higher RPM with similar torque if i only increase the volts. higher torque if i increase the amps. higher rpm and torque and rpm if i increase both volts and amps. but now i am not operating the motor at the rated 500W. i am operating it at higher power levels.

remember also that my output power is related to but not the same as my electrical power put into the motor. the motor and controller will never be perfectly efficient. there will be losses. to measure Hp i need to measure the and time the mechanical work done at the wheel.

now a Watt is a Watt regardless of whether it is electrical or mechanical. we just need the right formulas to convert one to the other.

1Hp = 745.8Watts. commonly rounded up to either 746 or 750W depending on how anal you want to be.
1Hp = 550lb-ft /sec
1Hp = 75kg-m /sec


to summarise:

1. 500W Motors are only 500W motors if run at the input power levels recommended by the manufacturer. most motors can and will run at higher power but with increased wear. better motors designs will tolerate more abuse.

2. Torque, RPM and Watts are all inter-related. Watts are the output power created by a given Torque at a specific RPM. if i increase the RPM i have to decrease the Torque to keep the Watts the same. conversely if i decrease the RPM, the Torque is increased.

rick

rkosiorek said:

This may be the least understood relationships in motors.

Click to expand...

Too right....

Here's the formula in SI units:

Power (Watts) = Torque (Nm) x Angular Velocity (radians per sec)

Angular Velocity = 2pi * 60 * rpm

So:
Watts = Nm * rpm * 2pi / 60
or
Watts = Nm * rpm * 0.105

Solved for torque:
Nm = Watts * 60 / rpm / 2pi
or
Nm = 9.549 * Watts / rpm.

HTB_Terry said:

In regards to the larger diameter motors having more torque, that's logical if all other variables are equal. For example, the Aotema with a smaller diameter than the 9C, has very similar torque due to larger magnets and a metal ring surrounding the magnets (verses Al) which magnifies the field. This compensates for the smaller diameter and is a more advanced design in my humble opinion. (full disclosure: my company sells the Aotema motor)

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In the interest of keeping information on this forum accurate, readers should note that all of the direct drive hub motors commonly available (Nine Continent motors, Crysatlyte motors, Golden motors, WE motors, etc.) have a steel ring around the magnets. In both the NC and Crysatlyte hubs, it's about 1/4" thick solid steel, and is responsible for the bulk of the rotor mass. The aluminum housing and spoke flange is cast over this ring, which I guess is why it might be mistaken for solid aluminum. Unless you have a halbach array of magnets, you need that steel ring!

Justin

Thank you everyone who contributed to these comments. I have learned a lot.

I was just wondering, if anyone with the background to be able to answer would be so kind to do so (I couldn't answer my own question by reading the comments)...

If local laws impose a restriction such as "a bicycle with an electric motor capable of generating up to 250 watts of power", is there a way to have a lower wattage, but higher torque and gearing to allow such a small capacity motor to pull a decent weight, up hill at an acceptable speed, and still maintain a decent speed on the flat?

ie. 5/10km/hour up a steep incline and perhaps 25/30km on flat?

Regardless of price ie ultra high voltage even if the batteries cost a lot, can this be done by choosing particular high/low voltage batteries, upping the amps etc?

I apologise if my terminology is not correct, but I hope you understand what I am asking. Taking my question to the extreme, purely to try to understand the measurement of electronics/motors/voltages etc, hypothetically could a 200w rated motor, with the right batteries, motor construction/winding/heat dissipation, voltage, amps etc, propel a 500kg bike uphill at say 30km/hr and reach speeds of 100km/hr on flat (this is not what I am after, but I think this hypothetic question may help me or other readers understand).

What I am looking to do is build a bike that can carry a decent load, tow a hiking/camping trailer, comply with maximum wattage laws, yet not crawl around at 1km/hr. Is this at all possible? Or is there no way to tweak the construction/componetns to achieve this without exceeding a wattage maximum?

In reality, I will have a bike setup of perhaps 200kgs with me, the bike (inc motors, battery etc and luggage as a total, and perhaps pull a trailer with an additional weight of approx 75kgs. I can incorporate an additional motor to the trailer to assist. I don't have a power restriction on the trailer, but do not want to rely on the power in the trailer to propel the bike, as most trips I would not be taking the trailer, only when my big labrador is coming with me.

The reason the bike weight will be high as I will require a larger battery than most as I would require it to have battery capacity for about 100kms with all of this weight.

Thank you in advance.
Andrew

Yes, gearing will help and under-sized or under-powered motor both lug up a hill and still achieve a reasonable top speed on the flat and explains the popularity of crank-drive production bikes, which are often limited to 250W and drive the motor through a bike's normal rear gear cluster.

UnderpantsAndy said:

Taking my question to the extreme, purely to try to understand the measurement of electronics/motors/voltages etc, hypothetically could a 200w rated motor, with the right batteries, motor construction/winding/heat dissipation, voltage, amps etc, propel a 500kg bike uphill at say 30km/hr and reach speeds of 100km/hr on flat

Click to expand...

You probably need to reduce those speeds by ~5 times to be an accurate reflection of what 200W is really capable of!

UnderpantsAndy said:

Taking my question to the extreme, purely to try to understand the measurement of electronics/motors/voltages etc, hypothetically could a 200w rated motor, with the right batteries, motor construction/winding/heat dissipation, voltage, amps etc, propel a 500kg bike uphill at say 30km/hr and reach speeds of 100km/hr on flat (this is not what I am after, but I think this hypothetic question may help me or other readers understand).

Click to expand...

Probably not. I have a 500W rated motor that I run at 2500W with lots of cooling mods, but it will still overheat if I push full power for very long. You can generally run about 2x the rated power on most motors if you keep track of the temps.

A really good way to see how fast you can go or how much it takes to go up a hill is to use the ebikes.ca simulator
https://www.ebikes.ca/tools/simulator.html

You can enter various parameters and get a good idea for what the bike would do under those conditions.

Want you are looking for is in one equation:

Power = Force X Velocity. Power is watts.

You need force to pull up a hill. If Velocity (speed) drops you can still climb that hill at low power. But you might climb slowly. Just like using lowest gear on your mountain bike.

This is physics, there is no getting around it. It sounds like you are hauling a lot of weight. That means if you want to keep power low you need low gears and you will go slow. If you want to climb hills fast you need power.

To give some feel on the numbers, 250W sounds low, but only a strong rider can sustain 250W for an hour. Plenty of bikers can manage 250W to get up a hill, but the you ease off. Professional bikers can hit 400W.

So 250W is a lot of power in bicycle terms, more than a typical rider can manage for long, but not that much more. So with a that in mind the next hurdle is gearing.

A rider will have an efficient speed that they spin the cranks. Too slow and you exhaust quickly and strain your knees. Too fast and you flail ineffectively. So a rider needs gears that match the terrain. Flat riding? One or three speeds is fine. San Francisco? You need low, low gearing, and up a steep hill you are rolling at walking speed and working hard. If you carry weight the gearing needs amplify.

Motors aren't so different. They have an rpm range with good efficiency, about 72% to 95% of no-load rpm will have motor efficiency 75% or better. Where does the 25% go? It is heating up your motor! Lug the motor too slow too long and your motor gets toasted.

You won't cook your motor in the low 95-100% rpm range even though efficiency is low. The motor back emf prevents it from drawing enough power to hurt itself, no matter how big your controller.

The two main ebike choices are hub motors and mid-drive, and their biggest difference is gearing. A mid-drive runs through your bike gears, and so long as 1st gear is low enough that you never bog the motor below 75% of no-load rpm you should be OK, especially if you stay below 500W. (25% of 500W is 125W, it is pretty easy to dissipate 125W of heat). 250W is another matter. To dissipate 250W details of motor construction, size, and how long you keep power high matter a lot.

Mid-drive runs through you bike gears, so as long as 1st gear is low enough to keep motor rpm above 75%. If you are climbing a mountain pass use a lower gear, but you should be OK. If your 1st gear isn't low enough you can get into trouble fast.

With Hub motors the bike gears don't keep rpm up. You basically have three approaches:

1. Use a hub gear with no-load rpm low enough so you don't drop below 75% of no-load rpm for more than minute or two. This means your top speed on the flat will not be impressive, but the motor will be there for you on a grade or against a headwind. The good part is that hub motors that can do this are small and light. 200 rpm is a good speed if you hit hills, but won't do the job carrying heavy loads or up long steep grades.

2. Use the xiongda XD 2-speed hub motor. In low I think it is about 125 rpm. It will winch you up quite a grade. 2nd gear gives decent speed on the flats. Still pretty small and light.

3. High-power direct drive. These hubs are big and heavy, but some can dissipate a lot of heat. Creating a lot of waste heat at the hub may waste battery, but if the motor can shed heat well enough you won't damage it. These are good for speed on the flat and can be a durable solution. Resistant to overheating, they don't run power through the bike drivetrain.

So just to run an example against the desired speeds and grades, of the power required, even if friction and rolling resistance is zero:

power = force x velocity

In this case the force is gravity and the velocity is the vertical speed (opposite the force). If we consider 10% a steep grade, then for every km, there will be 100 meters of vertical movement. So if you want to travel forward at velocity of 10 km/hr, then your vertical velocity is 1 km/hr, or 0.28 m/s.

So, since f=ma, and the mass is 200kg and a= 9.8 (meters/second squared; gravity), then
f= 1960 Newtons

So the power required to maintain 10km/hr on a 10% grade is
power = 1960 x 0.28 = 544 watts

so, if your motor is only 200 watt, then the fastest you could ride on a 10% grade is 200/544 x 10, or 3.7 km/hr, but realistically less due to friction and rolling resistance.

Probably worth noting that 544 is power at the wheel. Electrical watts into the motor would be 20-30% greater for a motor operating in its comfortable zone, but for a motor struggling along in its unhappy place could be 50% greater, or worse.

Also, knowing the thrust requirement (1960N) you can multiple by wheel radius (in metres) to get the motor torque required. Motors sometimes come with a maximum torque rating (or find the motor's Kt value and multiple by maximum phase current) so you can see if it's up to the job - as 10km/h up a steep represents a low speed/high load) scenario that some motors may not be able to handle, even if it can happily produce 500W at higher speeds (less torque (= current = heat) required)).

Or use the Grin Cycles simulator tool which can work out all this stuff for you

Also, cyclists being an anal lot, have measured the aero drag and rolling resistance for different bike/rider/tyre combos at different speeds and publish tables of how many Watts each scenario requires. You'll see things like "upright rider on mountain bike with knobbly tyres" compared to "velomobile on skinny tyres". Once you know the power for level ground you can just add in the power required for the elevation change as E-HP calculated above :thumb:

E-HP said:

So just to run an example against the desired speeds and grades, of the power required, even if friction and rolling resistance is zero:

power = force x velocity

In this case the force is gravity and the velocity is the vertical speed (opposite the force). If we consider 10% a steep grade, then for every km, there will be 100 meters of vertical movement. So if you want to travel forward at velocity of 10 km/hr, then your vertical velocity is 1 km/hr, or 0.28 m/s.

So, since f=ma, and the mass is 200kg and a= 9.8 (meters/second squared; gravity), then
f= 1960 Newtons

So the power required to maintain 10km/hr on a 10% grade is
power = 1960 x 0.28 = 544 watts

so, if your motor is only 200 watt, then the fastest you could ride on a 10% grade is 200/544 x 10, or 3.7 km/hr, but realistically less due to friction and rolling resistance.

Click to expand...

Exactly,
And since there are online calculators people who don't want to do less physics have an easy option. And the bike calculators have good estimates for friction and air resistance.

I use http://bikecalculator.com/
In your case if I input 200kg, 544W, and 10% grade it calculates 9kph, a bit lower because of the friction you mentioned.

In practice if I am climbing on the pedals I have trouble balancing if I go slower than 9kph. 6kph is OK if I am on the seat because the motor is helping. So there is a practical limit on how slow you can go. I'm not sure 200W total input is practical on a 10% grade.

I'm not sure grade estimates I see on ES are realistic (25%, etc.) I live in Seattle, we have some steep hills. Not quite San Francisco steep, but steeper than most places. 10% is about as steep as a Seattle hill gets in any sustained way, the killer hill on my commute is 8%. So I think 8% is a pretty good number to work to for Seattle-ish hills.

bikecalculator example

Punx0r said:

Or use the Grin Cycles simulator tool which can work out all this stuff for you

Click to expand...

The Grin simulator has some drawbacks:
1. The Grin simulator graphs are not standard. Motor performance sheets graph motor data against torque. They start a motor at no-load and apply increasing torque. Here is an Aikema example, I see the same format from various manufacturers:

I cannot find an option on the Grin simulator that will produce a motor graph in standard format.

2. Only some motors are in the Grin database. And since the Grin format is non-standard I cannot compare a motor to a motor that isn't on the Grin database even if I have motor data But I can use standard motor data to assess a motor against real work needs).

3. All the small hub motors Grin sells or lists in the database seem to be fast winds and bad choices if you live in a hilly area. So if you want a light small hub motor and need low gearing you cannot use the Grin simulator to weight your option. And options exist, there are very good small light hub motors that can climb hills, they just cannot be assessed on the Grin simulator.

I think it would be great if Grin had an option to make a standard motor chart. I would like it if they offered a discreet motor like the Bafang G310 in a slower wind. As it is the Grin simulator does not much help me pick out a motor or compare against other interesting motors.