Racing and efficiency

motomoto · Jun 8, 2016

I went to a national motocross recently (Hangtown) and I noticed that every rider is revving there engines
getting every ounce of acceleration out of their bikes. I mean, they are in the area of the power band that
makes the most horsepower. Which means they are in the proper gear for the speed they are traveling.

On ES we have a lot of 'Gurus' informing us that a gearbox is never needed, and all that extra useless weight
should be used for magnets and copper and battery.

So I want to look at 2 different aspects of this scenario. One is fastest possible acceleration and the other
is efficiency.

First efficiency. I will use arbitrary numbers. Lets say you have a motor that makes the most horsepower
at 8,000 rpm. It will rev more but the torque is dropping. The highest area on the horsepower curve is
between 6,000 and 9,000 rpm. I am going to leave voltage out of this example and look at amperage
because amperage produces torque and torque times rpm equals horsepower. To make this example
simple, lets say that at 100 amps the motor makes 10 horsepower at 1,000 rpm. At 2,000 rpm it make
20 horsepower and so on until the torque starts to drop off. For my 100 amps I want to be efficient,
so why would I run the motor at any rpm other than 6,000 to 9,000? At 1,000 rpm you are only getting
10 hp. At 8,000 you are getting 80 hp for your 100 amps.

Now on to power. Accelerating in high gear is slow. Torque from an electric motor is tremendous. High
numbers all the way across the graph. Terrific. But come on, not having it in the right rev range, so much
for your acceleration and lap times.

All the 'gurus' will say you just have to have this huge motor in your vehicle that breaks the tire loose at any rpm.
Well that is great, but then you've got the waste of amps thing going and not getting the most horsepower for the amps
you are putting into the motor. To me throwing a bunch of amps at a low rpm is a waste and is slow even though it
feels 'torquey'

Thud · Jun 9, 2016

Moto,
You are trying to mix oil & water....

motomoto said:
I went to a national motocross recently (Hangtown) and I noticed that every rider is revving there engines
getting every ounce of acceleration out of their bikes.revving does not make acceleration in of itself....they are only revving the motor to get it to produce the torque required in that situation....they may need to change ratio's to keep the motor in its torque producing part of the power band I mean, they are in the area of the power band that
makes the most horsepower. Which means they are in the proper gear for the speed they are traveling.By my observation, the gear is inconsequential, its simply a function of the power delivery map of the current engine....speed is relative.

On ES we have a lot of 'Gurus' informing us that a gearbox is never needed, and all that extra useless weight
should be used for magnets and copper and battery.In perfect world.....maybe LOL (I don't know any one who lives there)

So I want to look at 2 different aspects of this scenario. One is fastest possible acceleration and the other
is efficiency. this is a confusing comparison.....I think efficiency is the wrong term in this scenario...I will cover this in the wrap up

First efficiency. I will use arbitrary numbers. Lets say you have a motor that makes the most horsepower
at 8,000 rpm. It will rev more but the torque is dropping. The highest area on the horsepower curve is
between 6,000 and 9,000 rpm. I am going to leave voltage out of this example and look at amperage
because amperage produces torque and torque times rpm equals horsepower. To make this example
simple, lets say that at 100 amps the motor makes 10 horsepower at 1,000 rpm. At 2,000 rpm it make
20 horsepower and so on until the torque starts to drop off. For my 100 amps I want to be efficient,
so why would I run the motor at any rpm other than 6,000 to 9,000? At 1,000 rpm you are only getting
10 hp. At 8,000 you are getting 80 hp for your 100 amps.your scenario's don't accurately correlate to the power output of electric motors

Now on to power. Accelerating in high gear is slow.No, its not. Maximum acceleration is strictly a function of torque. the more you have, the faster you accelerate. My YZ125 launches in 1st gear, My CRF launches in 3rd gear. Top fuel guys launch in the only gear they have Torque from an electric motor is tremendous. High
numbers all the way across the graph. Terrific. But come on, not having it in the right rev range, so much
for your acceleration and lap times.Again, don't get hung on high revving 4 strokes....the rpm is a remnant of IC power delivery

All the 'gurus' will say you just have to have this huge motor in your vehicle that breaks the tire loose at any rpm.
Well that is great, but then you've got the waste of amps thing going and not getting the most horsepower for the amps
you are putting into the motor. To me throwing a bunch of amps at a low rpm is a waste and is slow even though it
feels 'torquey' A correct motor will provide the required torque without excessive/inefficient amperage flow.

I won't tell you to get a fat motor & battery for motocross performance....because I don't believe for a second that one solution is the final answer to every problem.
What we need is a motor that delivers the minimum amount of torque required to perform the required task...any more than that is "inefficiency"
if that motor will work over a broad-enough rpm range to deliver the performance required....problem solved. (assuming its a competitive weight...has a workable rotating mass.)
If its spinning to slow or too fast to give us the low & top speed required...we will need to have another ratio(s) available. (or as the gurus say....the correct motor.....whether it exists or not LOL)
The flip side of that is the horsepower you can get from a high power density (high revving) motor. This is where the ideology of gearing gets us back to modern ice designs.

I still say your going to need at min a 2-speed to get any electric I've seen competitive off-road. Still hoping to see different.
For apples to apples, I would love to see a graph of "rear wheel torque to the ground" that a top pro uses on a lap of a national track.
those are the #s we need to design to.

Don't get too hung up by the "Guru's" & the oft repeated "wrong motor for the job" these guys are a great resource for educational purposes. Its more about what you do with the information as its presented. & I don't know of any of them who spend any real time at the motocross track.

I would love to see what you could do with tripled up astro's, a rekluse clutch & a torque controlled auto shift....2, maybe 3 speeds

motomoto · Jun 9, 2016

Thanks for the response Thud. I have a YZ125 too. It's pretty fun. It feels like you are in hyper mode all the time.

I think I will give up on this thread. Thanks for your view.

nutnspecial · Jun 9, 2016

I thought it was a no-brainer.

Physics. Until 'E' can beat that, we can still find benefit. Gearboxes are awesome, and so is E

parabellum · Jun 11, 2016

nutspecial said:
I thought it was a no-brainer.

Physics. Until 'E' can beat that, we can still find benefit. Gearboxes are awesome, and so is E

Tell us about Tesla or Zero, or just about Lukes bicycle.

nutnspecial · Jun 11, 2016

Hopefully you are not serious - this has already been done to death in case you didn't know.

And I'm ok with physics dying too, but so far the motors, batteries, and vehicles still have to follow those laws of physicality, along with all it's little tricks like levers and wheels . . . get it?

Yes, benefits of variable gearing lessen as 'efficiency' increases, but no, it likely does not become obsolete until unity is reached. To think otherwise evidences a fanboy/shortsighted understanding/mentality that likely only holds back advancement towards such :|

Thud · Jun 11, 2016

on topic:
[youtube]JLdp1Kz0naI[/youtube]

E-motocross is coming.....There is some incredible urban motocross potential if we could stifle the noise a good race bike makes.

the KTM in this video is so close to being there (except in price)...not a frail bicycle conversion.....but really, still no match for a 12 year old expert on a yz85. We aren't going to get a 45 minute moto out of one either.

This thread was about efficiencies in a racing scenario....where my original thought about efficiencies wasn't about getting the best yield from a battery, but more to keeping motors in a survivable condition, in a motocross application.

Motocross isn't even the best test requiring a wide operational envelope.....cross-country enduro needs more low end power finess & about the same top end performance.

motomoto knows a thing or two about motocross.

nutnspecial · Jun 11, 2016

I imagine as special purposed bikes those are/will also be 'one speed'?

When I get on my gsx600 nowadays, I am underwhelmed by the acceleration and torque and annoyed at the same time by the accompanying noise. But, I do still love the cost vs range/performance etc etc etc of my petrol sport touring.

However, you know that old 'motor' trick with a soda can around the bike tire? It was pretty fun to make the ebike <highly> audible the other day. I went screaaaming (in terms of a can, knobbies, and xxxxwatts) thru the neighborhood for a change lol, and it made me miss my sx and rm 125s

thepronghorn · Jun 11, 2016

motomoto said:
I went to a national motocross recently (Hangtown) and I noticed that every rider is revving there engines getting every ounce of acceleration out of their bikes. I mean, they are in the area of the power band that makes the most horsepower. Which means they are in the proper gear for the speed they are traveling.

On ES we have a lot of 'Gurus' informing us that a gearbox is never needed, and all that extra useless weight should be used for magnets and copper and battery.
Mostly just magnets and copper.

So I want to look at 2 different aspects of this scenario. One is fastest possible acceleration and the other is efficiency.

First efficiency. I will use arbitrary numbers. Lets say you have a motor that makes the most horsepower at 8,000 rpm. It will rev more but the torque is dropping. The highest area on the horsepower curve is between 6,000 and 9,000 rpm. I am going to leave voltage out of this example and look at amperage because amperage produces torque and torque times rpm equals horsepower. To make this example simple, lets say that at 100 amps the motor makes 10 horsepower at 1,000 rpm. At 2,000 rpm it make 20 horsepower and so on until the torque starts to drop off. For my 100 amps I want to be efficient, so why would I run the motor at any rpm other than 6,000 to 9,000? At 1,000 rpm you are only getting 10 hp. At 8,000 you are getting 80 hp for your 100 amps.
The problem is, to get 80hp out you need to put 80hp in but to get 10hp out you only need 10hp in. You need to realize that it is phase amps that create torque, not battery amps. Using your numbers, to make 10hp at 100amps and 1000rpm, your controller's duty cycle will be a lot lower since you have much less BEMF so you do not need nearly as much voltage into the motor to get your 100amps. Lower duty cycle = less power out of your battery.

Phase current = (Vbat - Vbemf) / Rwinding

To make 80hp at 100amps and 8000rpm would take a lot higher duty cycle / phase voltage since the BEMF at 8000rpm is 8x higher than it was at 1000rpm. This higher duty cycle might just end up being about 8x higher than the 10hp one. See how it all works out?

Now on to power. Accelerating in high gear is slow. Torque from an electric motor is tremendous. High numbers all the way across the graph. Terrific. But come on, not having it in the right rev range, so much for your acceleration and lap times.

All the 'gurus' will say you just have to have this huge motor in your vehicle that breaks the tire loose at any rpm. Well that is great, but then you've got the waste of amps thing going and not getting the most horsepower for the amps you are putting into the motor. To me throwing a bunch of amps at a low rpm is a waste and is slow even though it feels 'torquey'.
As I explained above, there is no waste of amps. That's why trading gearing weight for copper/magnet weight is better.

edited to remove a less pertinent example, you can still see it if you want in the edit history...

I went back and read Thud's comments, and they are mostly spot on. I can't claim to have ever been to a motocross track, but I do believe that even if it doesn't exist right now, a motor could be designed (and built) that would meet your torque, rpm, and weight requirements. I think you already looked at the EMRAX motor and had some problems purchasing one, but they can be had because people are using them in the real world, and the EMRAX is probably pretty close to meeting a lot of your specs.

motomoto · Jun 11, 2016

Thud said about the EMX race.

still no match for a 12 year old expert on a yz85

That race is so pathetic. I can't stand to watch it. Just wimpy ass electric. I'm ashamed.

motomoto · Jun 12, 2016

So I have been studying this subject of electric motors and one gear or multiple gears for racing purposes because
I want to make fast dirt bikes. In Formula E racing the winning team has gone to a 2 speed from last years spec
5 speed with the first gear only used at the start or out of very slow turns. The second place team has 3 speeds
and several have 1 speed.

This is my take. One speed will be the ultimate, someday. However, it takes lots of development. For now, with
what I want to do with dirt bikes, a play bike can be 1 speed, a serious motocross bike, 2 speeds.

liveforphysics · Jun 12, 2016

They have multiple gears because they are fixed using that multi-speed transmission case and gears on the shaft if they use it or not.

What you actually want is more torque available at the rear wheel than you can ever use, and to have that torque available for the entire speed range you wish to travel.

It's entirely possible to have that with an electric motor and a fixed ratio, and if you care about efficiency it's possible to have the absolute lowest losses with direct drive. Every power transfer or conversion equals inherent loss. The motor itself can be designed around making the conversion from electricity to the force desired at the rear wheel in a single conversion step. This will not be able to be improved upon by multiple conversion step solutions, as they can only mean the application hasn't found the correct motor if they show benefit.

tangentdave · Jun 12, 2016

To throw another idea into the mix, what if we're limited in the amount of current available? Most practical systems have an upper limit, especially the tiny systems we use for ebikes. With an upper motor torque limit, now it makes sense to use a gearbox to get the max torque available for different vehicle speed ranges.

The vehicle also has a threshold torque in each situation, this may be getting started on a hill or achieving the desired acceleration. Power applied that produces less torque than the threshold torque is wasted (for the case of getting started). Shouldn't the system design be trying to achieve this threshold torque as quickly/easily as possible?

When I'm getting started on a steep trail, 500W in a low gear will do it, pull me right up. In a tall gear, the motor requires full throttle overheating things, draining the battery and still not making enough torque to pull me up. On a flat road my point is mitigated, but trails and motocross tracks ain't flat. Combined with our limited battery capacity, the vehicle needs to make the most of the situation. IMHO.

-dave

diff_lock · Jun 12, 2016

tangentdave said:
To throw another idea into the mix, what if we're limited in the amount of current available? Most practical systems have an upper limit, especially the tiny systems we use for ebikes. With an upper motor torque limit, now it makes sense to use a gearbox to get the max torque available for different vehicle speed ranges.

The vehicle also has a threshold torque in each situation, this may be getting started on a hill or achieving the desired acceleration. Power applied that produces less torque than the threshold torque is wasted (for the case of getting started). Shouldn't the system design be trying to achieve this threshold torque as quickly/easily as possible?

When I'm getting started on a steep trail, 500W in a low gear will do it, pull me right up. In a tall gear, the motor requires full throttle overheating things, draining the battery and still not making enough torque to pull me up. On a flat road my point is mitigated, but trails and motocross tracks ain't flat. Combined with our limited battery capacity, the vehicle needs to make the most of the situation. IMHO.

-dave

Limited battery current? How tiny is tiny? Zero FX runs direct drive via single belt reduction. How steep is steep?

liveforphysics · Jun 12, 2016

tangentdave said:
To throw another idea into the mix, what if we're limited in the amount of current available? Most practical systems have an upper limit, especially the tiny systems we use for ebikes. With an upper motor torque limit, now it makes sense to use a gearbox to get the max torque available for different vehicle speed ranges.

The vehicle also has a threshold torque in each situation, this may be getting started on a hill or achieving the desired acceleration. Power applied that produces less torque than the threshold torque is wasted (for the case of getting started). Shouldn't the system design be trying to achieve this threshold torque as quickly/easily as possible?

When I'm getting started on a steep trail, 500W in a low gear will do it, pull me right up. In a tall gear, the motor requires full throttle overheating things, draining the battery and still not making enough torque to pull me up. On a flat road my point is mitigated, but trails and motocross tracks ain't flat. Combined with our limited battery capacity, the vehicle needs to make the most of the situation. IMHO.

-dave

Motor current is phase current. Battery current is a nearly unrelated power input source to the controller to buck down to whatever current it needs.

For deathbike to send ~650A RMS phase current to my motor for a launch at 0rpm it draws ~7A from the battery.

Your battery current is related directly to the power you're making, and motor torque is related to the phase current. If you want to make big torque at low speeds, it's minimal power because power is a function of RPM*torque.

parabellum · Jun 12, 2016

Maybe someone should finally just take same motor as Luke and beat him with multi-stage transmission on quarter mile and only then start spitting BS about awesome gearboxes, not even mention weight limit. It is beat to dead in dozens of treads, even numerically and graphically and conclusion is, gear box= patch solution for shitty motor/controller combo, not made for the task from ground on. My god, how often will this come up?

tangentdave · Jun 12, 2016

I know what 1000W feels like in low gear and what it feels like in high gear. My battery is only so big and I'd rather only use 1000W in a low speed situation than say 3000W from a gear 3x as tall in the same low speed situation. I need the same amount of wheel torque regardless the gearing. Why would I gear my bike for a fast race track when I know I'm going to be on the slow track? The straightaway is only so long, why do I want gearing taller than that when I'm trying to beat you to the corner?

motomoto · Jun 12, 2016

Luke please explain the numbers

For deathbike to send ~650A RMS phase current to my motor for a launch at 0rpm it draws ~7A from the battery.

thepronghorn · Jun 13, 2016

tangentdave said:
I know what 1000W feels like in low gear and what it feels like in high gear. My battery is only so big and I'd rather only use 1000W in a low speed situation than say 3000W from a gear 3x as tall in the same low speed situation. I need the same amount of wheel torque regardless the gearing. Why would I gear my bike for a fast race track when I know I'm going to be on the slow track? The straightaway is only so long, why do I want gearing taller than that when I'm trying to beat you to the corner?

That's weird because power = torque x rpm, so if you are getting 3x the torque at the rear wheel at the same rear wheel rpm, then you are probably putting in ~3x the power...

motomoto said:
Luke please explain the numbers

For deathbike to send ~650A RMS phase current to my motor for a launch at 0rpm it draws ~7A from the battery.

Click to expand...

https://en.wikipedia.org/wiki/Buck_converter

http://www.allaboutcircuits.com/technical-articles/buck-converters-and-their-cool-applications/

Basically a motor controller acts like a buck converter when it is driving motors at less that full duty cycle so it steps down voltage while stepping up current. If Luke's controller output full pack voltage to the motor windings at 0rpm when there is no back emf, the current would be around 100V / 0.001ohm = 100000A. Note: I pulled the 0.001ohm winding resistance out of thin air although it's probably within an order of magnitude of the correct figure. In order to limit the current to 650A RMS, the controller PWM's the windings to input (probably a sine wave) with an RMS voltage around 650A x 0.001ohm = 0.65V to each phase.

tangentdave · Jun 13, 2016

What we could really use in the EV world is a device that reduces the vehicle's load as applied to the motor as much as possible. It's great that Tesla and Deathbike can use 2000A and 650A for drag racing but the battery I want to carry won't support that much power for very long. I need to reduce the power needed for each situation as much as possible if the vehicle is going to have acceptable range and performance.

To put it another way, I don't wanna be in top gear the whole ride, man. The arguments for no transmission are centered around power conversion in the motor. The transmission lowers the load on the motor. This lower load either extends range by achieving the same vehicle performance at lower speeds with less current or allows higher wheel torque for the same current as a direct drive setup. When I'm racing you to the corner or trying to clear the double right out of the turn, I don't want to be in top gear. I can get better acceleration and enough range to finish the race with a few gears to choose from.

Systems that can't carry a trunk full of batteries have to reduce the load on the batteries they can carry. I might also bet Tesla would be using a transmission if they had one tough enough. Starting your car in 4th gear on a San Fransico hill is silly. Modern ICEs make enough torque over a power band as wide as many electric systems (6000RPM), why aren't we all driving a single speed, high-stall torque converter automobile? Pushing more and more current through a single speed electric system is akin to installing a larger displacement ICE in your car so you can skip the transmission.

Many vehicles will best fit their purpose as a single speed, many vehicles will better fit other purposes with a transmission.

liveforphysics · Jun 13, 2016

Some folks still don't get that it's less burden on your battery.

If you had a lower ratio gear you could shift into, this would get the motor BEMF higher and draw more power off the pack.

If you have an EV with gears, and you want to pull the most current from your pack, then start in 1st gear. If you want to pull the least current start in 4th gear (or whatever you have ).

nutnspecial · Jun 13, 2016

Ok, so after dave's very 'tangible' post, you concede nothing eh?

Wowsers :lol: I'm out!

riba2233 · Jun 13, 2016

tangentdave said:
What we could really use in the EV world is a device that reduces the vehicle's load as applied to the motor as much as possible. It's great that Tesla and Deathbike can use 2000A and 650A for drag racing but the battery I want to carry won't support that much power for very long. I need to reduce the power needed for each situation as much as possible if the vehicle is going to have acceptable range and performance.

To put it another way, I don't wanna be in top gear the whole ride, man. The arguments for no transmission are centered around power conversion in the motor. The transmission lowers the load on the motor. This lower load either extends range by achieving the same vehicle performance at lower speeds with less current or allows higher wheel torque for the same current as a direct drive setup. When I'm racing you to the corner or trying to clear the double right out of the turn, I don't want to be in top gear. I can get better acceleration and enough range to finish the race with a few gears to choose from.

Systems that can't carry a trunk full of batteries have to reduce the load on the batteries they can carry. I might also bet Tesla would be using a transmission if they had one tough enough. Starting your car in 4th gear on a San Fransico hill is silly. Modern ICEs make enough torque over a power band as wide as many electric systems (6000RPM), why aren't we all driving a single speed, high-stall torque converter automobile? Pushing more and more current through a single speed electric system is akin to installing a larger displacement ICE in your car so you can skip the transmission.

Many vehicles will best fit their purpose as a single speed, many vehicles will better fit other purposes with a transmission.

Do you know that fastest accelerating ICE/hybrid car today doesn't use transmission?

Thud · Jun 13, 2016

Another perfect example of no one reading the op.....

Does any one here think the KTM in that video is anything other than weak sauce? (or remotely competitive with a modern 4-stroke 250cc ice on a real course?)

You can spout off about single speed all day & be right.....but no one can produce a list of parts to assemble a real Moto crosser that could compete heads up. there isn't a motor/battery/controller combo that will get the job done.....even for a 15 minute moto.

This is why Kim abandoned this thread....too much theory & no data that supports his(& mine) specific interests or constraints.

thepronghorn · Jun 13, 2016

tangentdave said:
What we could really use in the EV world is a device that reduces the vehicle's load as applied to the motor as much as possible. It's great that Tesla and Deathbike can use 2000A and 650A for drag racing but the battery I want to carry won't support that much power for very long. I need to reduce the power needed for each situation as much as possible if the vehicle is going to have acceptable range and performance.

Phase Current does NOT equal battery current
Torque is related to Phase Current
Power out is proportional to battery power into the controller
Deathbike uses 650A from the controller but only 7A from the battery for a launch because the controller bucks down the battery voltage to get whatever phase current it wants - the controller turns 100V, 7A from the battery into 1V, 700A going to the motor
Your battery does not care how many phase amps are flowing to the motor because all it feels are the 7A that are being pulled from it
Gearing lower does not help your efficiency because while the required motor torque decreases, your motor has to spin faster in your lower gear to make the rear wheel spin at the same speed, so the total power out to the wheel which is the same as the power out of the battery is the same regardless of gear ratio(minus various inefficiencies)

To put it another way, I don't wanna be in top gear the whole ride, man.
cool
The arguments for no transmission are centered around power conversion in the motor.
okay
The transmission lowers the load on the motor.
not really, more gear ratio means less phase current but more rpm, the power has to be made somehow
This lower load either extends range by achieving the same vehicle performance at lower speeds with less current or allows higher wheel torque for the same current as a direct drive setup.
range is not extended; only if you keep phase current the same then lower gearing = more torque
When I'm racing you to the corner or trying to clear the double right out of the turn, I don't want to be in top gear.
This all assumes that you have a limited amount of phase current/motor torque to use which means you're using a motor-controller combination that is too small for your intended application.
I can get better acceleration and enough range to finish the race with a few gears to choose from.
Imagine not needing the gears since your motor will output the torque needed to spin the wheel at all times with whatever reduction ratio you choose to build your bike with.

Systems that can't carry a trunk full of batteries have to reduce the load on the batteries they can carry. I might also bet Tesla would be using a transmission if they had one tough enough. Starting your car in 4th gear on a San Fransico hill is silly. Modern ICEs make enough torque over a power band as wide as many electric systems (6000RPM), why aren't we all driving a single speed, high-stall torque converter automobile? Pushing more and more current through a single speed electric system is akin to installing a larger displacement ICE in your car so you can skip the transmission.

Many vehicles will best fit their purpose as a single speed, many vehicles will better fit other purposes with a transmission.

nutspecial said:
Ok, so after dave's very 'tangible' post, you concede nothing eh?

Wowsers :lol: I'm out!

There's nothing to concede. The math isn't very hard. It's just ohms law and basic motor theory.

Edit: previous example drew the wrong conclusion and had some minor numbers mistakes.
Say we have a motor that spins 10k rpm no load at 100V which means its Kv is 100 rpm/V and its Kt is 0.0954 Nm/A. Suppose its internal resistance is 0.01 ohm. Say our controller is limited to 100A, so we can make 100A * 0.0954Nm/A = 9.5Nm of torque. This 100A takes 100A * 0.01ohm = 1V of voltage drop in the windings to make.

Now say we're in 3rd gear, our motor is spinning at 1000 rpm, so our BEMF is 10V.
To make 9.5 Nm of torque from our motor, 10V bemf + 1V drop = 11V into the windings.

Now say we have the same motor in 1st gear which has a ratio 3x lower than 3rd gear. Now our motor is spinning at 3000 rpm to get the same rear wheel rpm, so our BEMF is 30V.
To make 9.5 Nm of torque from our motor, 30V bemf + 1V drop = 31V into the windings.

Our first gear allows us to draw more power off the pack since bemf is higher. We can accelerate faster, but it's also less efficient. If we only need 9.5Nm of torque to spin our rear wheel, why not just leave the bike in 3rd gear? It's not super difficult to get a motor that can make the torque to spin the wheel and also spin fast enough to propel us as fast as we want to go.

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