The Great "Gearing vs Hub Motor" Debate

[safe]

Revised Results

Okay the "revised" numbers are now:

First Gear: 0-15 mph in 2.16 seconds with an energy "cost" of 3 kiloWatts. (3,219 Watts) (0.06% of a 1440 Watt/Hour Pack)

Fifth Gear: 0-15 mph in 3.25 seconds with an energy "cost" of 4 kiloWatts. (4,367 Watts) (0.08% of a 1440 Watt/Hour Pack)

The net "waste" for the "hub motor" gearing is 1147 Watts or an excess waste of power to the tune of 36%. (same as before more or less)

Note: I was trying to use the torque figures and it's just much easier to go directly off the Power(in) and Power(out) values. The proportions are the same and now the numbers for seconds are more realistic. The power is also more realistic. This one acceleration would equal a "waste" of 0.02% of the power supply of a 1440 Watt hour battery for this 1200 Watt motor at a 60 amp current limit if it was run in fifth gear rather than first.

You also "lose" 1.088 seconds in acceleration. It's both SLOWER and more WASTEFUL.

 

[Leeps]

Could you graph that with time as the x axis and speed as a dependent variable it would be easier to read.
Joe

 

[Lowell]

How long does each gear change take? Do you think you could shift at full power (3000W?) or would you have to let off the throttle.

 

[safe]

How long does each gear change take? Do you think you could shift at full power (3000W?) or would you have to let off the throttle.

Drag racers shift once to complete their quarter mile times with their gas powered motors and they often have well over a thousand horsepower. The present internal hubs (like Sturmey Archer) are going to be able to handle about 1000 Watts to 1500 Watts, so for "legal power limit" vehicles this would be enough. "Speed Shifting" might be adding more stress to these present day hubs that is wise to do. My current shifting (with a derailler) takes less than a second to complete and I simply "blip" the throttle closed momentarily. (you need the power on, but it doesn't need to be full... I've "Speed Shifted" by accident before and it survives, but it's not a good idea)

I think I'm stressing a philosophical point more than anything that gears ALWAYS give better acceleration at a lower energy cost than having to start out in high gear and "torque" your way up to the "real" powerband that doesn't start until about 30 mph. From 0-30 mph the power is low(er) and the efficiency is poor(er).

In the future, if these "macho bikes" with big horsepower (above 2 hp) become in fashion, I'm sure that companies like Sturmey Archer or others would build internal hubs specifically for these needs. It's also possible to place the transmission with the motor itself (which is actually a better idea) and the history of motorcycle transmissions is that they have become very reliable. Technical problems can always be solved if you put your mind to it.

So let's solve the "ideal" case first and then get to "pragmatic" issues later. My bikes are all going to be "legal" in the motor power area because I'm hoping to possibly sell these things one day... (maybe)

Give me some time with these spreadsheets. I've got to refine then and automate them better so that I can add variables and perform better "what if" scenarios. Things like "hill climbing" performance comparisions would be good (in both speed and energy losses) because that's more static. Give me some more time to "dig" through the mountains of data...

 

[safe]

Could you graph that with time as the x axis and speed as a dependent variable it would be easier to read.

This is time on the y-axis and the x-axis is related to the gear ratio so for a low gearing each increment translates to a smaller speed jump and the higher gearing translates to a big jump in speed. My spreadsheet is based on rpm so since we are talking about the DIFFERENCE that gearing makes to rpm you have to account for it somehow. (maybe I'll find some better way to express it later)

Anyway... this is the time it takes for the bike to accelerate from 0-10 mph in each of the first five gear options. So the idea is that you START in one of the gears and use it as a "hub motor" like fixed gear. There's no "shifting" in this chart... it's just "fixed gear" performance at various gear ratios. This shows the advantages of proper gearing over an excessively high gear. (like one that would get you to 50 mph) This "should" be intuitively obvious because just like with a car you place it into FIRST get to get going and then shift to FIFTH gear on the freeway to get top speed. (somehow people with electric bikes think they can reinvent the laws of physics! )

The numbers are:

First Gear - 1.89 seconds @ 2621 Watts.

Fifth Gear - 2.85 seconds @ 3679 Watts.

Time saved in first gear - 0.959 seconds (85% delay avoided)

Energy saved in first gear - 1058 Watts. (40% waste avoided)

And you do this at EVERY stop... so the DIFFERENCE adds up over time...

 

[safe]

If all things were equal and you were in a race then the person using gears would get the "jump" off the line and get into the first turn ahead of the rider that used a fixed gear. While the "leader" might have to "shift" at some point if he is already physically ahead on the track then you would expect that once top speeds were reached that the geared bike would be in the lead already. Of course once up to speed you can slipstream to pass, but the point is that you begin the race "last" and that's not always a good thing if passing is difficult. If there were 20 riders going into the first turn and 19 had gears and you had a fixed hub motor you would probably be the last one into the turn... of course all bets are off if unlimited power is allowed. Double the size of the motor and all the figures change, so I'm strictly talking about equal sized motors... "all things being equal" gears are better... the "hemi" concept still can win because it uses more raw power...

 

[Matt Gruber]

in 1972 i was so persuaded by a similar argument, i replaced the 3.23 open rear in my '70 318 duster with a 4.56 posi.
this really impressed my friends!
so we went down the 1/4 mile drag strip and,
guess how much quicker the et was?

 

[safe]

Here are the numbers for 0 - 20 mph. Notice how little difference there is from 10 - 20 mph in the numbers as far as losses. By the time you get above 10 mph things start to equalize:

The numbers are:

First Gear - 2.39 seconds @ 3826 Watts.

Fifth Gear - 3.61 seconds @ 5069 Watts.

Time saved in first gear - 1.22 seconds (61% delay avoided)

Energy saved in first gear - 1243 Watts. (32% waste avoided)

Note: This should answer your dragstrip question... it's only a one second advantage... but one second at every stop and the extra power saved is just one of MANY arguments for proper gearing. (ultimate top speed is another along with overall efficiency improvements) You pick up little savings everywhere you can...

 

[safe]

Thought Experiment

Let's say you take a one hour ride on suburban streets. Every minute you have to stop at a stop sign. (a realisitc reality in my town) So if we add up all the time lost and power lost of a hub motor over a geared bike we get:

Time lost - 60 stops - 1 second lost per acceleration - One minute lost overall.

Energy lost - 60 stops - 1000 Watts lost per acceleration - 60,000 Watts lost overall.

Since a 1440 Watt Hour battery holds 1440 * 60 * 60 = 5,184,000 Watts of energy then the percentage of the battery "lost" over that hour is only 1%.

Other than SPEED lost you really only lose 1% of your energy supply... so don't panic, it's not that bad...

 

[xyster]

Hubmotors with more than one winding, like the 408/4012,408/411,406/409 simulate the effect of having two gears. The higher # winding setting generates more torque for the same power and has better efficiency at lower rpms compared to the lower winding #.

 

[xyster]

Energy lost - 60 stops - 1000 Watts lost per acceleration - 60,000 Watts lost overall.

Since a 1440 Watt Hour battery...

This is meaningless. You have to calculate the energy lost in watt-hours (not watt/hours and not watts) to compare it to the energy in the battery as measured in watt-hours.

 

[safe]

This one is kind of interesting. The "limit" of no load speed for first gear is 32 mph, so this shows how well below that your first gear "starts to get exhausted" and you need to upshift. See the red curve start to rise at the end... that's the powerband "peaking" and dropping down the other side...

 

[safe]

This is meaningless. You have to calculate the energy lost in watt-hours (not watt/hours and not watts) to compare it to the energy in the battery as measured in watt-hours.

A "watt hour" is one watt for one hour worth of energy. So if you take the battery in total it can provide it's watt hour rating times sixty minutes, times sixty seconds since watts are based upon seconds. (one amp, one volt, one second)

The percentage is what matters... there's ONLY a 1% loss over an entire hour of standard riding and that's not that bad... so relax... the losses aren't terrible...

60,000 Watts equals 16.67 Watt hours of energy... (but I see your point... is that 60,000 Watts over a second or over some other interval... I'll have to check my spreadsheet)

I'm back... the 1000 Watt loss occurs over a period of the "lost" one second of accelleration. So the numbers are good... the 60,000 Watts can be viewed as being associated with "roughly" a second. All is fine. (close enough)

So it's 60,000 Watt/Seconds... verses 1440 Watt/Hours...

 

[safe]

The higher # winding setting generates more torque for the same power and has better efficiency at lower rpms compared to the lower winding #.

It would be interesting to see the "range" that they can get on that. I'm finding that you "ideally" need a "range" of roughly 300% to be able to achieve the best results. So if a hub motor could achieve that "range" of "perfected" power then it could be able to replace gears entirely.

300% is the "desired" range from everything I've learned so far... (at least for speeds from 0-60 mph and horsepower below 2 hp)

A three speed should suffice... 100%, 200%, 300%... (in gearing terms 1 to 1, 1 to 2 and 1 to 3) ...but it's the range that matters. You have to cover all those gear ratios (the range) whether you do it with three gears or like in my case it will be eight gears.

 

[safe]

Hill Climbing Ability (Part 1)

The Parameters:

1200 Watt Unite motor with 60 Amp controller and all the usual (for me) numbers for weight, aerodynamics etc. The "test" is a one mile uphill that has a (steep) 10% slope. This is about the biggest hill you will ever find, so that's a good way to really know what the differences are going to be. As with previous examples I will use gears 1st thru 5th with 5th gear being the "equivalent" to a hub motor since it can reach 50 mph. I also include wind resistance as a factor, however, it doesn't seem to have a large effect.

Let's go through this one at a time...

The first chart is "Rpm Based 10% Slope" which basically gives an idea of how the tall gearing forces the motor to run at lower rpms. While a "massive" motor might be able to pull at it's peak rpm, anything less than this 1200 Watt motor willl not. So this shows how the high gears force you to "bog down" a small motor.

 

[safe]

Hill Climbing Ability (Part 2)

The second chart is for "Speed and Time" on the 10% hill climb. Since a faster moving bike (using the lower gear) gets to the top of the hill quicker you actually save energy while the slower tall gear must waste energy taking longer.

 

[safe]

Hill Climbing Ability (Part 3)

The third chart is "Watt Hours" for the 10% slope hill climb. Basically you take the Power(in) and Power(out) values which are based in units of "seconds" and figure out the time it takes each gear to reach the top. From that you can get a total Watt Hour figure to achieve the task of climbing the hill.

 

[safe]

Hill Climbing Ability (Summary)

Okay... so what?

In first gear it takes about 3 minutes to reach the top of the hill and it uses a total of 110 Watt Hours to get there with a "waste" of 40 Watt hours.

In fifth gear it takes about 8 minutes to reach the top of the hill and it uses a total of 197 Watt Hours to get there with a "waste" of 131 Watt hours.

In terms of time you save 5 minutes. (it takes over twice as long in 5th gear)

In terms of energy you save 87 Watt Hours. (the last 4 Watt hours are lost due to wind resistance at the higher speed for 1st gear)

While a hub motor with massive "hemi" styled energy could literally "lift" itself out of the low rpm nightmare, the typical small motor cannot do this and finds itself wallowing in pain. This is exactly what I've felt on my bike when I run the "tall gears" and try to climb one of the steeper hills in my neighborhood. If I switch back down to the "low gears" then not only do I climb the hill with ease, but also much faster. So low gears for hills are very beneficial. (it's not just acceleration that gearing helps)

What's "funny" here is that the bike in first gear could probably ride to the top of the hill and turn around and ride back down again until he meets up with the bike in fifth gear, then turn around and race back up again and still win and still use the same or less energy. The "tortiose" loses in this contest... the low geared bike wins easily...

 

[Mathurin]

18 people have contributed to this topic, posts by safe represent 43.6% of total posts.

 

[xyster]

Posts by safe: 72, 43.6% of total posts in this topic excluding the present.

Wow, I'm way behind Oh well, most of mine are responses to Safe's. Hmmm....that chart also shows who has a life, who doesn't, and by what relative percentage they do or don't. 8)

 

[lemmiwinks]

I'm in a graph! Woohoo!

 

[safe]

It won't be long until the temperature warms up... then it's time for me to actually build stuff again.

I'm in my "research mode" now... (I've learned a lot in these 6 weeks of intense study)

You have to admit that the "Hill Climbing" (article) was pretty good. It took some effort to figure out, but it does pretty much prove the gearing point.

 

[fechter]

Is there a way to calculate points made per post? Maybe words typed per point made. We could create a simulator to predict the graph.

Safe- we all love you.
I spend a good part of my job explaining very technical things to very non-technical people. It's a skill worth developing.

 

[xyster]

Safe- we all love you.

The Fechmaster's crop from his mountain hide-away must have just come in today.

We know ... it's medical. Probably necessary for that scooter-induced back injury.

8)

 

[safe]

When I get "on a roll" with an idea I go at it hard for a couple of days. But tomorrow will be the warmest day of the week so I'll be getting a ride in and I don't have any other ideas right now. There's nothing that I'm trying to figure out at the moment...