## Difference in acceleration with different voltage?

michielk   1 mW

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Joined: Jun 08 2017 6:14am

### Difference in acceleration with different voltage?

Hello guys,

Optional long introduction
A few weeks ago I (successfully) build my first e-bike! I used a locally made classic style bike with steel frame, no suspension, 28" wheels. Motor is Crystalyte 4065 rear wheel hub motor (High Torque), Controller is 24-48V 40A sensorless and I used 60 Panasonic NCR18650B cells to create a 10S 6P 37V 20Ah battery pack and control the motor with a half twist regulator. The bike is setup with a single (high) gear (freewheel). Top speed is just shy over 20mph and thanks to the high torque motor it accelerates nicely and goes over bridges/hills with ease.

I would like to build a full suspension freeride e-mountainbike (26" wheels) as well for some off-road fun and just messing about. For hardware I would use the same motor (Crystalyte 4065) but with a 48-72V 45A controller. I have not decided on what Voltage I would run the bike at, but have a question concerning this.

Specs
Motor: Crystalyte 4065 (3000W; 24-72V; 50Amp max; 8 RPM/V; Max Torque 55-120Nm) in a 26" wheel + Controller 48-72V 45A
Target: 25MPH top speed with quick acceleration / climbing ability (MTB)
Battery 1 : 91x NCR18650B 13S 7P 48,1V 23Ah 47Amp max (48V * 45A = 2.160W theoretical max output)
Battery 2 : 96x NCR18650B 16S 6P 59,2V 20Ah 40Amp max (60V * 40A = 2.400W theoretical max output)
Battery 3 : 120x NCR18650B 20S 6P 74,0V 20Ah 40Amp max (74V * 40A = 2.960W theoretical max output)

Actual question
According to the spec sheet of the motor; 48V is sufficient to reach 25mph. Will there be a noticeable increase in acceleration or climbing ability if I opt for a higher voltage battery? The motor is rated for 3000W, so I assume with 48V * 45A I would only be able to use 2.160W ? To use it's full potential of 3.000W I would need to use a 74V * 40A setup?

I'm not trying to build a motorcycle or break any records. I just want something fun and reliable.

Thanks!
Kind regards, Michiel.

fechter   100 GW

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### Re: Difference in acceleration with different voltage?

You will have some increase in torque and acceleration with a higher pack voltage. The controller is limiting to 45A at the battery, so with a higher pack voltage, you will be dumping more watts into the motor with a higher pack voltage. Torque is really a function of the motor phase current, but you will get a little more with a higher voltage.
"One test is worth a thousand opinions"

teklektik   10 GW

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### Simulator Battery Comparison / Adjusting Kv

Use the CA simulator when possible. Very accurate and much better than subjective or anecdotal evidence.

michielk wrote: Battery 1 : 91x NCR18650B 13S 7P 48,1V 23Ah 47Amp max (48V * 45A = 2.160W theoretical max output)
Battery 3 : 120x NCR18650B 20S 6P 74,0V 20Ah 40Amp max (74V * 40A = 2.960W theoretical max output)
Your Xlyte 4065 is not in the simulator but the alternate wind 4080 model is so we can just adjust the simulator to convert its model of a 4080 into a 4065 using Kv adjustment. Looking at the specs (http://www.crystalyte.com/The%20Crown.htm) for these two motors, we use the unloaded data to determine the Kv of each then figure out the ratio to get an adjustment factor:

Xlyte4080to4065KvCorrection.png (151.32 KiB) Viewed 880 times

With the motor model set up in the simulator, we just need to pick a battery and controller that match the battery proposals. Here's a couple comparison runs with the highest voltage battery as System A and the lowest voltage as System B. The battery and controller were configured as:
• The batteries are filled in using a 'Custom Battery' choice with a per-cell nominal voltage of 3.75V/cell, then working out the pack voltage from the series string.
• Controllers have two limits: 'rated' (battery) current and 'phase' (motor) current. While a controller is limiting battery current, it can deliver more phase amps at lower voltage to the motor than it draws from the battery - so we need two current limits. The controllers are filled in using a 'Custom Controller' choice and limited to the battery max current to protect the battery. The Phase current is set to 2.5X the controller limit as a common Infineon-style setup. (Otherwise, choose limits as appropriate...)
The bike is set up using ho-hum generic MTB settings - your weight and posture may vary.

The top speed results on the flat without pedaling are:

Xlyte4065BattSpeedComparison.png (112.13 KiB) Viewed 880 times

Here some of the interesting settings and results are highlighted (I used a very slightly different 4080->4065 correction factor when I took the snaps - not worth doing new pics).

(1) Not surprisingly the high voltage battery smokes the low voltage one with a top speed about 10mph faster. A rule of thumb says you can comfortably cruise at 80% of top speed since the motor won't be spun out and will still have some throttle response left - so about 20mph and 28mph for these two cases. Interestingly, the 48V bike is predicted to hit 25mph as the motor manufacturer claimed....

(2) Next, the higher voltage/higher capacity pack appears to have a shorter range, but that is running at WOT in this image and so the higher speed creates more drag and eats power for the highV bike. If you were to re-run the simulation with partial throttle on the highV bike (about 63%) so its speed matched the top speed of the lowV bike (and so had the same drag), you would see the high capacity pack had a proportionately longer range.

Here you need to look at available Whr of the batteries. So:
• 72V pack --> 20Ah * 72V = 1440 whrs
• 48V pack --> 23Ah * 48V = 1104 Whrs
So at the same speed the 72V pack is going to have very roughly 1440/1104 * 100 = 130% the range of the 48V pack.

(3) Finally, you need to scrub the cursors along the X-axis to get different accelerations assuming you are slamming it WOT off the line. Here's a sample of what the accelerations would be as you blew by 10mph.

Xlyte4065BattAccComparison.png (111.9 KiB) Viewed 880 times

Again, no surprises - although the controller matched with the lower voltage battery (System B) has a higher max phase current limit, neither controller curve shows the controllers are running into their max phase current limits (red output power curves have only one point of inflection instead of two) so the max phase current settings in the controllers really don't matter in this case - just the controller rated (battery) current limits. But we know that the controller with the higher input power is going to have the higher output power (red curve) and thus the higher phase amps at any given speed. Since phase amps translate into torque (blue lines), the higher voltage (and higher phase amp) bike out-accelerates the low voltage bike by over 30% and will similarly climb hills better.
• EDIT - There is a tiny bit of phase amp limiting going on with the higher voltage battery under 5mph. Although the added inflection point is barely noticeable in the red power curve, we see it pretty plainly in the blue torque curve as the flat horizontal fixed torque due to phase amps being held to a limit in the 0-5mph range (torque is directly proportional to phase amps). In this example this is due to the controller 100A phase limit not the controller 40A rated limit.
So - your proposed higher voltage, higher capacity pack will have a higher top speed, greater range, and will out-accelerate the low-voltage pack.

As you can see, the controller is playing a critical role when the controller is limiting (the bike is under load accelerating or climbing hills) and where it can provide more phase amps according to the power limit (the red power curves to the left of the inflection point). The part of the curves to the right of the inflection point are where the controller is no longer limiting; there we see the raw motor characteristics play against the battery directly with essentially no effect by the controller. Translation - available battery power and controller limits are primary factors in motor performance for acceleration/hill climbing.

You can mess around with this setup here to see what happens on hills (speed, how long it will take overheat, etc):
http://www.ebikes.ca/tools/simulator.ht ... &throt=100

Anyhow, just a quickie look at your proposals....
Last edited by teklektik on May 16 2018 10:37am, edited 6 times in total.
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michielk   1 mW

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### Re: Difference in acceleration with different voltage?

Thanks for that quick reply mate!

Seriously, thanks so much for taking the time to calculate the exact numbers.
This should be added to the FAQ!

My gut feeling would have guessed the higher voltage would improve climbing ability/torque, but I had no idea on how big of a difference it would make.

I will definatly get a controller that is able to do 48-72V @ 45A. I will most likely start with a 48V battery (cost, weight, already have a BMS on the way). After comparing acceleration to my current bike I can evaluate and rebuild the battery to a higher voltage (adding batteries).

Thanks so much!
Kind regards, Michiel.

michielk   1 mW

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Joined: Jun 08 2017 6:14am

### Re: Difference in acceleration with different voltage?

In the mean time I bought my bike, but now noticed a H4065 engine will not fit the bike (different mounting axle system). Everything is possible, but it will be very time consuming and expensive to adjust for this. Now I'm looking at a mid motor, specifically the Bafang BBSHD 1000Watt. Even though the power seems to be lower, I will be able to use the gears on the bike, so I assume I will be able to climb steep hills and also reach a good top speed. The bafang is limited to 52V.

atarijedi   100 W

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### Re: Difference in acceleration with different voltage?

In BLDC motors, torque and thus acceleration is a function of current. So voltage won't effect acceleration.

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### Re: Difference in acceleration with different voltage?

atarijedi wrote:
May 15 2018 11:55am
In BLDC motors, torque and thus acceleration is a function of current. So voltage won't effect acceleration.
Yes it will. Current is reduced by back-EMF as the motor speed increases. If your battery voltage is higher you can maintain higher currents before back-EMF starts reducing them.

It's quite noticable when comparing my ebike with a 44V battery compared to my friend's which has an identical motor, controller and wheel size, since his battery is 36V.

atarijedi   100 W

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### Re: Difference in acceleration with different voltage?

May 15 2018 12:06pm
atarijedi wrote:
May 15 2018 11:55am
In BLDC motors, torque and thus acceleration is a function of current. So voltage won't effect acceleration.
Yes it will. Current is reduced by back-EMF as the motor speed increases. If your battery voltage is higher you can maintain higher currents before back-EMF starts reducing them.

It's quite noticable when comparing my ebike with a 44V battery compared to my friend's which has an identical motor, controller and wheel size, since his battery is 36V.
As BEMF increases, voltage across the windings drops, current flowing into the motor drops. That limits top speed, but not acceleration, which is a function of torque, which is a function of current.

All else being equal, 36V motor running at 10A will accelerate at the same rate as a 48V at 10A, it's just that the 36V motor will hit its top speed sooner and stop accelerating. But acceleration is the rate of change of speed, which will be the same, that is separate from the top speed.

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### Re: Difference in acceleration with different voltage?

atarijedi wrote:
May 15 2018 1:33pm
As BEMF increases, voltage across the windings drops, current flowing into the motor drops. That limits top speed, but not acceleration, which is a function of torque, which is a function of current.

All else being equal, 36V motor running at 10A will accelerate at the same rate as a 48V at 10A, it's just that the 36V motor will hit its top speed sooner and stop accelerating. But acceleration is the rate of change of speed, which will be the same, that is separate from the top speed.
Yes, this is just a matter of how you think about it. Peak acceleration and torque will be the same but the higher voltage system will be able to maintain it's peak acceleration at higher speeds than the lower voltage system.

teklektik   10 GW

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### Re: Difference in acceleration with different voltage?

atarijedi wrote:
May 15 2018 11:55am
In BLDC motors, torque and thus acceleration is a function of current. So voltage won't effect acceleration.
Wrong (in this case), as the plots above illustrate.

You are confusing battery current with phase current and ignoring the details of the exact proposal. In this particular case the critical point is that available battery power increased along with battery voltage because the battery current changed very little.

The higher available input (battery) power allowed the controller to deliver higher phase amps and hence higher torque. It was essentially incidental that the power increase came from increased voltage, but in any case the increased torque is not directly related to battery current - it is related to phase current.
Last edited by teklektik on May 15 2018 7:07pm, edited 1 time in total.
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atarijedi   100 W

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### Re: Difference in acceleration with different voltage?

May 15 2018 2:09pm
atarijedi wrote:
May 15 2018 1:33pm
As BEMF increases, voltage across the windings drops, current flowing into the motor drops. That limits top speed, but not acceleration, which is a function of torque, which is a function of current.

All else being equal, 36V motor running at 10A will accelerate at the same rate as a 48V at 10A, it's just that the 36V motor will hit its top speed sooner and stop accelerating. But acceleration is the rate of change of speed, which will be the same, that is separate from the top speed.
Yes, this is just a matter of how you think about it. Peak acceleration and torque will be the same but the higher voltage system will be able to maintain it's peak acceleration at higher speeds than the lower voltage system.
Being able to maintain acceleration (rate of speed increase) isn't the same as having a higher acceleration (higher rate of speed increase). Thus, acceleration does not increase with voltage.

parajared   10 kW

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### Re: Difference in acceleration with different voltage?

What are you all even talking about? Your operating voltage has absolutely nothing to do with acceleration... zilch. The repulsion on the magnets is what dictates torque. All the motor cares about is wattage.

I guess you guys haven't heard of 36 volt 700 amp golf carts? The kind that haul four fat dudes and their golf clubs down the golf course.

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### Re: Difference in acceleration with different voltage?

atarijedi wrote:
May 15 2018 7:02pm
Being able to maintain acceleration (rate of speed increase) isn't the same as having a higher acceleration (higher rate of speed increase).
If I can maintain high acceleration over a certain time period where a lower voltage system is starting to have weaker acceleration, then my acceleration over that time period is higher in comparison.

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### Re: Difference in acceleration with different voltage?

parajared wrote:
May 15 2018 7:26pm
What are you all even talking about? Your operating voltage has absolutely nothing to do with acceleration... zilch.
noun: acceleration
the rate of change of velocity per unit of time.

If you're only looking at the initial acceleration then sure, operating voltage doesn't change that if it's kept within reason.

If you're comparing different systems and looking at their acceleration from 0-30 km/h for example, systems with voltage too low will have worse acceleration.

parajared   10 kW

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### Re: Difference in acceleration with different voltage?

Acceleration is dictated by two things
1) magnetic repulsion in guass on the magnet side
2) wattage on the electrical side

The magnets don't care what kind of repulsion they are getting. It can be volt heavy, it can be amp heavy. 10amps 20 volts of repulsion is the same as 20amps 10 volts of electromagnetic repulsion.

atarijedi   100 W

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### Re: Difference in acceleration with different voltage?

May 15 2018 8:09pm
parajared wrote:
May 15 2018 7:26pm
What are you all even talking about? Your operating voltage has absolutely nothing to do with acceleration... zilch.
noun: acceleration
the rate of change of velocity per unit of time.

If you're only looking at the initial acceleration then sure, operating voltage doesn't change that if it's kept within reason.

If you're comparing different systems and looking at their acceleration from 0-30 km/h for example, systems with voltage too low will have worse acceleration.
The higher voltage system will be able to accelerate for a longer period of time, but it won't have a higher rate of change of speed. Max acceleration will be at 0V, and is dictated by the motor constants, and since the motors are the same, and torque (acceleration) is dictated by Kt = Nm * A, they will have the same torque and acceleration.

I think we are saying the same thing, just in different ways.

parajared   10 kW

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### Re: Difference in acceleration with different voltage?

If you're comparing different systems and looking at their acceleration from 0-30 km/h for example, systems with voltage too low will have worse acceleration.
No, that's wrong
assuming the magnets are the same size a 100 watt motor that's operating at 12volts 20kv for 240rpm is the exact same thing as a 100 watt motor that's operating at 48v 5kv for 240 rpm.

It's just that the lower voltage motor will have fatter phase wires, larger esc, larger battery wires.

parajared   10 kW

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### Re: Difference in acceleration with different voltage?

I think you are confusing manufacturer availability with physics.

The tendency is for manufacturers to make lower voltage motors for lower wattage setups. A manufacturer could totally make a 72 volt system that is only really capable of outputting a few hundred watts if they wanted to.

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### Re: Difference in acceleration with different voltage?

I didn't word that well. I'm not talking about different motors, or the same motor with different kv.

With a single motor, if I run it with a higher voltage battery and the same phase current, I will be able to maintain max acceleration for longer.

Comparing the two setups side-by-side, by the time the low voltage system reaches it's maximum speed, the higher voltage system will be at a higher speed. Over that time, the higher voltage system had greater acceleration.

Alan B   100 GW

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### Re: Difference in acceleration with different voltage?

michielk wrote:
May 15 2018 11:13am
In the mean time I bought my bike, but now noticed a H4065 engine will not fit the bike (different mounting axle system). Everything is possible, but it will be very time consuming and expensive to adjust for this. Now I'm looking at a mid motor, specifically the Bafang BBSHD 1000Watt. Even though the power seems to be lower, I will be able to use the gears on the bike, so I assume I will be able to climb steep hills and also reach a good top speed. The bafang is limited to 52V.

The BBSHD is a good selection and straightforward to install as long as it fits your bottom bracket. Putting power through the gears will significantly increase the torque for climbing and provide high top speeds, depending on the gearing available. It does put a lot of stress and wear on the chain and gears so they will require more maintenance, but it makes it much easier to change tires and repair flats, and the bike will be lighter compared to a 3000W hubmotor.

Regarding the postings after that, there are some serious misunderstandings in many of them regarding voltage and current in BLDC systems. Keeping the controller, motor and battery current constant, raising the battery voltage will raise both top speed and peak acceleration, as confirmed by the simulation. Assuming the controller is only limiting battery current, the increased voltage will increase motor current, torque and acceleration at low speeds. Torque and acceleration is a function of motor current, not battery current. At low speeds the motor current is much higher than battery current due to the power conversion taking place in the controller. At low speeds the motor requires low voltage and the excess voltage is converted to additional motor current. The controller acts like a buck switching regulator. Frequently a current multiplication value of 2.5 is used but this is not a fixed factor, the actual value changes with battery voltage and system speed and can be much higher at very low speeds where maximum motor current and torque occur, which drives the acceleration. Many folks here call motor current phase current instead, but they are just different names for the same thing.

As anyone who has actually changed from a 36V to a 48V or 72V battery will tell you, the increase in acceleration and hill climbing torque is huge.

Enjoy your new BBSHD, it is an entirely different approach to powering an ebike. It has both advantages and disadvantages. I have very similar setups with the CroBorg being a large hubmotor and the Ridge Runner being a BBSHD setup. You can read about them via links in my signature below.

Have fun, ride safe and welcome to ES.

LockH   100 GW

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### Re: Difference in acceleration with different voltage?

ES changed my life (for the waaaaay better).

Eff. June, 2014 Phoenix Ebike Promotions

(Current ride? High speed lawn chair.)
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parajared   10 kW

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### Re: Difference in acceleration with different voltage?

As anyone who has actually changed from a 36V to a 48V or 72V battery will tell you, the increase in acceleration and hill climbing torque is huge.
The problem with this statement is that it's dead wrong. Someone who doesn't understand BLDC theory is going to read this and mistakenly buy the wrong product or build their e-bike wrong because of this. Your statement is going to cost someone money.
Comparing the two setups side-by-side, by the time the low voltage system reaches it's maximum speed, the higher voltage system will be at a higher speed. Over that time, the higher voltage system had greater acceleration.
The same can be said of higher KV though.

parajared   10 kW

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### Re: Difference in acceleration with different voltage?

The only way what you are talking about is true is if we are talking about the OP's specific motor. In that case yes, the additional voltage will help on that specific motor.

teklektik   10 GW

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### Re: Difference in acceleration with different voltage?

Alan B wrote:
May 16 2018 7:30am
Regarding the postings after that, there are some serious misunderstandings in many of them regarding voltage and current in BLDC systems.
+1 (notably excepting AlanB's overview)

Not only hijacked a thread about a simple comparison of two specific battery packs, but the hijacking is filled with misinformation. Not recommended reading.
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parajared   10 kW

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### Re: Difference in acceleration with different voltage?

Not only hijacked a thread about a simple comparison of two specific battery packs, but the hijacking is filled with misinformation. Not recommended reading.
And what about the right to speak your mind? You can't just falsely accuse someone of hijacking. It's not hijacking if you are trying to stop the spread of mis-information. I want a best quality information to be available to the public, just the same as you.

Concepts of operating voltage are being inaccurately represented. Just because my viewpoint doesn't align with yours doesn't mean I should be disbarred from your conversation. I would hope the next time I mis-represent something that you would "hijack" my thread and set me straight. I would rather be set straight than wander around like a dummy saying something that's not true.