Formula for acceleration times? (Split from: Beginner: Falcon vs T4)

[Mono]

4 hours ago, on one said:

I didn't mean that @Krozin should consider buying a V8 only as a learner wheel. Being a measly 32 lbs it's a niche wheel for

The current V8F (the V8 is not produced anymore) has a stronger axle but weighs actually 37.2 lbs (16.9 kg).

4 hours ago, on one said:

I just looked at the ratio for T4, 100v/2500 watt !!

LOL, this is how rumours are created 

Watt divided by Volt is Ampere, you are just saying here that the T4 is specified by 1 / 25A. BTW, torque is directly proportional to motor current, that is, the lower Volt/Watt, the more torque  I know, it's utterly confusing...

...but think about this way: keeping Watt fixed, then increasing the Voltage increases the speed and decreases the torque while decreasing the Voltage decreases the speed and increases the torque.

Edited July 24 by Mono

[on one]

1 hour ago, Mono said:

LOL, this is how rumours are created 

Watt divided by Volt is Ampere, you are just saying here that the T4 is specified by 1 / 25A. BTW, torque is directly proportional to motor current, that is, the lower Volt/Watt, the more torque  I know, it's utterly confusing...

Okay, this is exactly what I want to clarify. I am processing this so please to help me get to a number "t" that corresponds to the 0 to 50km time that will make considerations for 3 basic wheel characteristics: Wheel tire size (w), motor watts (m), and battery volts (b).

Compare 3 wheels: OG Sherman (t=2.91 seconds as per Kuji), Ninebot Z10 (t=?), King Song 14D (t=?)

I will measure myself a few times on my Z10 and my 14D to provide my actual 0-50km time in seconds.

Then we can derive a formula that corresponds to the actual 3 recorded times.

For the OG Sherman, it's easy we already have all the data: w=20" m=2500 b=100 t=2.91

For the Ninebot Z10: w=18" m=1800 b=52 t=?

For the King Song 14D: w=14" m=800 watts b=67 volts t=?

So my question to the community is what is the formula for solving for time? Then I can make a real world test for the time (t) with my personal wheels and compare my real world data to our agreed upon formula.

[darn, I just realized I can't do the 0-50km time test on my wheels because they don't go that fast]

Still, we should be able to make a formula just based on the og sherm data.

 

Edited July 24 by on one
correction v for b

[on one]

Okay, progress, I was communicating with my personal assistant who provided me with an approximation for acceleration time 0-50km for Begode t4 of about 2.3 seconds.

 

My assistant is rather verbose, but here was her rationale:

To use the formula we derived earlier to estimate the acceleration time aaa for the Begode model T4 wheel, where t=16"t = 16"t=16", w=2500w = 2500w=2500 watts, and b=100b = 100b=100 volts, we'll use the empirical formula:

a=k⋅(tt0)p⋅(ww0)q⋅(bb0)ra = k \cdot \left( \frac{t}{t_0} \right)^p \cdot \left( \frac{w}{w_0} \right)^q \cdot \left( \frac{b}{b_0} \right)^ra=k⋅(t0t)p⋅(w0w)q⋅(b0b)r

We already have the values for the OG Veteran Sherman wheel as a reference:

• OG Veteran Sherman: t=20"t = 20"t=20", w=2500w = 2500w=2500 watts, b=100b = 100b=100 volts, a=2.91a = 2.91a=2.91 seconds.

Now, let's apply this to the Begode model T4:

Given:

• t=16"t = 16"t=16"
• w=2500w = 2500w=2500 watts
• b=100b = 100b=100 volts

Assuming t0=20"t_0 = 20"t0=20", w0=2500w_0 = 2500w0=2500 watts, b0=100b_0 = 100b0=100 volts (these are the reference values from OG Sherman),

We need to estimate kkk, ppp, qqq, and rrr to find aaa for the Begode model T4.

Since we don't have specific values for ppp, qqq, and rrr, let's make an initial estimation or assumption that the ratio of acceleration times might roughly scale similarly for different wheels of the same type under similar conditions.

Let's approximate aaa for Begode model T4:

a=2.91⋅(1620)p⋅(25002500)q⋅(100100)ra = 2.91 \cdot \left( \frac{16}{20} \right)^p \cdot \left( \frac{2500}{2500} \right)^q \cdot \left( \frac{100}{100} \right)^ra=2.91⋅(2016)p⋅(25002500)q⋅(100100)r

Simplifying this assuming p=q=r=1p = q = r = 1p=q=r=1 (initial estimation without more data):

a≈2.91⋅(1620)⋅1⋅1a \approx 2.91 \cdot \left( \frac{16}{20} \right) \cdot 1 \cdot 1a≈2.91⋅(2016)⋅1⋅1

a≈2.91⋅0.8a \approx 2.91 \cdot 0.8a≈2.91⋅0.8

a≈2.328 secondsa \approx 2.328 \text{ seconds}a≈2.328 seconds

So, based on this rough estimation with p=q=r=1p = q = r = 1p=q=r=1, the estimated acceleration time aaa for the Begode model T4 wheel could be approximately 2.3282.3282.328 seconds.

Please note, without exact coefficients ppp, qqq, and rrr, this is a simplified estimate. For a more accurate prediction, empirical data or further analysis adjusting these coefficients would be necessary.

 

Edited July 24 by on one
correction 2.3 seconds for the T4 0-50km

[Mono]

16 hours ago, on one said:

So my question to the community is what is the formula for solving for time?

The answer is very simple: there is no such formula which is correct in general. I am pretty sure of that, because you have neglected important parameters. For a start, the freespin speed of the wheel is one of them (that's obvious, if the freespin speed is 40km/h, the time to reach 50km/h is infinite regardless of 20kW power), the weights of wheel and rider are two others. There may be more: an electric motor needs three parameters to be (more or less completely) described and you gave only one, so after adding the freespin speed (or the speed of nominal power) one parameter is still missing (it may be negligible, I don't see this out of my head).

On the other hand, using the torque profile of the wheel over speed, it should be relatively straightforward to write a program to compute the acceleration time depending on the combined weight of wheel and rider assuming the rider can create the torque (which isn't necessarily a given, that's another equation to solve, probably relatively straight forward though). Unfortunately, I currently don't have free time to write this kind of code.

 

Edited July 25 by Mono

[on one]

I'm sorry, @Krozin, I am unable to provide you with a similar number value for the Falcon's 0-50km acceleration to compare because no comparable value for watts is provided, rather only max watts is provided :-/

[on one]

@Mono , don't worry about it. We already have the formula:

it works

Edited July 24 by on one
clarifying the formula

[meepmeepmayer]

I split this off into its own thread.

On this topic: no matter how often you look at motor wattage numbers, they still tell you basically nothing

Also, EUCs are self-balancing, which means either they just do what the rider forces them to do, or they crash if they can't keep up. There's nothing for the wheel to decide other than that. The lean determines the necessary acceleration to stay balanced. Now how hard or easy it is to lean a wheel depends on wheel geometry, firmware response, and whatnot.

The motor wattage tells you pretty much nothing about that. At best, it allows you to get some power limit of the wheel. Still tells you nothing about acceleration times.

[on one]

Thanks Meep! Now I am hoping @Kuji Rolls could actually do the Begode T4 0-50km acceleration test to help prove my proposed formula. Kuji? I bet you can’t make the T4 0-50km in 2.2 seconds!

[Mono]

10 hours ago, on one said:

We already have the formula:

Can't you see that the formula can't possibly be correct because it does not account for the motor speed? You could have two 100V 7kW motors, one with a freespin speed of 45km/h and another with a freespin speed of 90km/h. The formula computes the same acceleration time while the first motor will never even reach 50km/h.

Your assistant speaks elaborately but understands very little. Even without looking at the domain interpretation, the formula contains some funny things: the parameters t0, w0, b0 are entirely superfluous, the equation can be rewritten such that these parameters are all absorbed into k.

With domain interpretation: assuming that q=1 as your assistant did to my understanding, or any q>0 for that matter, means the acceleration time increases with increasing motor power, which is nonsensical.

10 hours ago, meepmeepmayer said:

no matter how often you look at motor wattage numbers, they still tell you basically nothing

I would say "nothing" is quite a bit exaggerated. For good reasons, I am sure we both would never buy, for ourselves, an EUC with a 500 Watt motor, so, here we go, Wattage does say something. Wattage is also ingrained in EU legislation for pedal assisted electric bicycles. I am sure we also can agree that increasing wattage of a system is likely to reduce the acceleration time and increase the maximal speed, when all else remains equal. But it's for sure not enough to make reliable acceleration time predictions.

Edited July 25 by Mono

[on one]

@Mono Please help me prove or disprove my formula using another EUC using real world 0 to 50 times. I don't have any reason at all to doubt that it's probable that Kuji's best time for the Begode T4 would be ≈ 2.3 seconds. This makes sense to me because the reason @Kuji Rolls could make a better time with the T4 than the OG Sherman is attributable to the 16" tire on the T4 compared to the 20" tire on the OG Sherman where Kuji made the 0-50km acceleration in 2.9 seconds.

If you won't help me prove or disprove my formula then offer me a new formula to prove. Otherwise, I think you are just sort of making noise with you minor considerations and still won't offer an improvement on my formula based off of your minor considerations. If my formula isn't useful then Kuji's T4 run will prove that, and then I will improve my formula.

 

Edited July 25 by on one
ttypo

[on one]

3 hours ago, Mono said:

Can't you see that the formula can't possibly be correct because it does not account for the motor speed?

My formula will never be correct or incorrect, rather useful for extrapolating the 0-50km acceleration potential of a given wheel where battery volts, motor watts, and tire size are known.

I understand that motor watts is a problematic number, battery volts is somewhat less problematic, and tire size is an accurate number. I'm totally open to adding a variable for free-spin time to cut-out which would seem to improve the usefulness of my formula, however, calculating that number, free-spin time to cut-out seems really difficult to measure.

Edited July 25 by on one
forgot a word

[meepmeepmayer]

3 hours ago, Mono said:

I would say "nothing" is quite a bit exaggerated. For good reasons, I am sure we both would never buy, for ourselves, an EUC with a 500 Watt motor, so, here we go, Wattage does say something.

Completely correct, it acts as a basic plausibility check. That's why I added the weasel word "basically"

3 hours ago, Mono said:

Wattage is also ingrained in EU legislation for pedal assisted electric bicycles.

I'm very convinced this is just because lawmakers are stupid and use it as a (bad) proxy for acceleration or top speed (in big part to sabotage anything satisfying feeling that would compete with cars, given by the fact that these legislations came long after electronic control means were available - but that's another topic).

3 hours ago, Mono said:

I am sure we also can agree that increasing wattage of a system is likely to reduce the acceleration time and in)crease the maximal speed, when all else remains equal.

Yes. In practice this is true. But we are still talking about self-balancing vehicles, so it is indirect: the firmware (and the entire wheel) will be designed so it matches the given motor (instead of easily overpowering it), and this determines that it accelerates well (or not). Theoretically, a determined "mean leaner" could still accelerate any wheel the same (until it gives up balancing, which may be earlier or later).

My point here is: there should be a fundamental difference between self-balancers and other vehicles. The motor power number of a EUC (if it even means anything) is either "plenty enough" or "clearly not enough", and further distinctions really say very little. For regular old vehicles, this may be different, and more of a continuous distinction. I guess?

3 hours ago, Mono said:

But it's for sure not enough to make reliable acceleration time predictions.

Exactly! As long as everyone agrees to that, I'm very happy.

[Mono]

2 hours ago, on one said:

I don't have any reason at all to to doubt that it's probable that Kuji's best time for the Begode T4 would be ≈ 2.3 seconds.

Right, however, a broken clock is right two times a day too. That's how it goes, a single such number tells us very little about the quality of the model.

2 hours ago, on one said:

If you won't help me prove or disprove my formula then offer me a new formula to prove.

Nice one. BTW, I did disprove your formula by a counter example (that's how disproving goes).

2 hours ago, on one said:

Otherwise, I think you are just sort making noise with you minor considerations and still won't offer an improvement on my formula based off of your minor considerations.

I gave very specific comments, besides and on top of the counter example. One key to "derive" formulas (AKA models) that match reality is understanding. I tried to give insights, but it seems that I failed. Fair enough, understanding takes time, people study months or years to get a good understanding of a domain and/or of maths. There are no real shortcuts for this.

2 hours ago, on one said:

If my formula isn't useful then Kuji's run will prove that, and then I will improve my formula.

Apparently you don't like to accept the very real possibility that there exists no such formula which could serve as a reasonably reliable estimate (or that none of us would find it even when we were trying as hard as we could for years, as multiplying input parameters will certainly not cut it). That's one thing we learn during studying too, hopefully: it's important to understand that some problems are not solvable and trying hard will mainly or solely become a timesink. It's an important aspect of problem solving to (i) have a good grasp on which these problems are and (ii) be able to let go.

25 minutes ago, on one said:

adding a variable for free-spin time to cut-out

I was referring to the freespin speed, which is given in many data sheets and also relatively easy to measure.

Anyways, thanks for your time trying and have fun.

Edited July 25 by Mono

[meepmeepmayer]

For the record, I do think trying to find a purely empirical formula for predicting acceleration/0-50 times is an interesting endeavor. I don't believe the "theory" (we presume to be) behind EUCs necessarily makes this somehow impossible. So much is in firmware, which will behave similarly each time (I guess?).

It's just really hard. How do you get reliable data to compare different wheels? Will you get a curve that allows predictions, or do you need so much data that it only tells you what you already know?

Edited July 25 by meepmeepmayer

[on one]

I love that you made this point, Mayor of Meep Meep Town,

15 minutes ago, meepmeepmayer said:

'm very convinced this is just because lawmakers are stupid and use it as a (bad) proxy for acceleration or top speed (in big part to sabotage anything satisfying feeling that would compete with cars, given by the fact that these legislations came long after electronic control means were available - but that's another topic).

And @Mono , your idea to create a variable for free-spin speed is welcome, even though the probablilty of looking at a broken clock and the clock being correct the first time you look is quite slim.

[Mono]

16 minutes ago, meepmeepmayer said:

I'm very convinced this is just because lawmakers are stupid

I can't believe you took the bait 

To my understanding, such laws are not written by lawmakers but by gremiums of experts. Lawmakers just ratify the text. In this case, the law was also incredibly successful which kinda doesn't make it look too stupid.

[Mono]

5 minutes ago, on one said:

I love that you made this point, Mayor of Meep Meep Town,

And @Mono , your idea to create a variable for free-spin speed is welcome, even though the probablilty of looking at a broken clock and the clock being correct the first time you look is quite slim.

In this case it seems more like you first moved the hands of the clock and then took a look, so you got the correct time but the clock still isn't moving.

Either way, in my experience, it's happening way more often than one would expect (and obviously we never literally look at a broken clock where we know the probabilities).

[on one]

23 minutes ago, Mono said:

Apparently you don't like to accept the very real possibility that there exists no such formula (or that none of us would find it even when we were trying as hard as we could for years) which could serve as a reasonably reliable estimate.

There exists such a formula, aforementioned in this thread. Now if Kuji would bless us and just do the acceleration test already.

[meepmeepmayer]

11 minutes ago, Mono said:

To my understanding, such laws are not written by lawmakers but by gremiums of experts.

Ok, for me, lawmakers = people who write the law. Including the bureaucracy behind it (let's not call them experts lol).

12 minutes ago, Mono said:

In this case, the law was also incredibly successful which kinda doesn't make it look too stupid.

Now that nonsense is truly bait.

Anyways, it's a different topic.

[Mono]

3 minutes ago, meepmeepmayer said:

(let's not call them experts lol).

My point was to say that at least some of them are domain experts, not law writing "experts".

And yes, we predictably disagree: I believe the law and its success does reflect this expertise (and to some extend the understandable lack of expertise for EUCs) and you have a totally different opinion on this.

[on one]

I'm thinking about producing a new formula that I can measure and test with my own 2 wheels: KS14D and Ninebot Z10.

The variables that I can directly observe are: tire size, battery volts, maximum free-spin speed and 0-20km time. This will provide me a number by which I can think about what it would mean.

[on one]

Then, @Mono I will extrapolate the data to your wheel if you would provide the data for your wheel, then I will be able to judge the predictability of my new formula. What's your wheel model and free-spin speed @Mono ? I will try to predict your 0-20km time.

Edited July 25 by on one
forgot a sentence

[Mono]

4 minutes ago, on one said:

Then, @Mono I will extrapolate the data to your wheel if you would provide the data for your wheel, then I will be able to judge the predictability of my new formula. What's your wheel model and free-spin speed @Mono ?

Sorry, I am out, I am sure you will find other people who are happy to participate.

[on one]

So, I'm kind of hurt, @Mono, I guess you are only on board for mostly insulting me and arguing with me, but you would rather not participate in anything that would lead to something creative. I suppose it's just as well. I can do this one on my own with my 14D and then extrapolate and test my Z10. That way the rider variable will be consistent. Thanks for helping me get this far with my formulas, you did help, I won't deny that.

[Mono]

14 minutes ago, on one said:

I guess you are only on board for mostly insulting me and arguing with me

Yeah, this impression of yours supports my conjecture that I haven't invested my time well. It's nothing personal, it's just one of these projects where it's better to avoid the sunk cost fallacy.