safe

I'm still in the process of getting all the necessary parts of the simulation program working correctly, but I thought I'd start off the thread and get people discussing the ideas.

"Regen" is short for "regenerative braking" and there are those that swear it's the greatest thing since sliced bread. However, there are some downsides to using regen that should be considered if you have a choice of regen verses just using a freewheel. (obviously many people cannot "choose" so regen becomes an option of last resort)

Here are some images to look at and ponder. A freewheel is faster than regen because when you coast without any regenerative braking taking place you go faster. This is what happens when the two types go down a hill. If you are like me and want to actually get somewhere in a hurry (sport riding) then regen seems to offer little benefit.

.

safe

Hmmmmm... no responses...

Are there no people that have wondered what "regenerative braking" really does?

The simple answer is that you in effect apply a brake in places (like a hill or the middle of a straight away) where you would not normally think of applying one. It's the act of braking that gives the recharge to the battery. For a sport rider the brakes are only used for sharp turns... unless a hill is extremely steep people just never use the brakes. So the core philosophical problem with regenerative braking verses a freewheel is that if you ride like normal people ride (only braking rarely) you have little chance to use it.

In something like the Tour De France race you see those guys pedal up these long hills and then on the downhills they just freewheel all the way down. For the regenerative braking folks they think:

"Aha! You could use the regen on the downhill!"

But you would be mistaken because it would be the equivalent of riding the brakes down the hill all the way. By the time you reached the bottom you might be 5-10 minutes behind the leaders and even if you recaptured some energy you would have to make that up somehow. It's really hard to make up 5-10 minutes of time because that means you have to go faster... which means more losses.

In the end the whole concept falls to pieces.

The only way it can make sense is if you are "okay" with taking much longer to get somewhere.

From the technical standpoint the equations that apply to the motor in the forward direction are the same equations that apply in the reverse direction. A motor can either work as a motor or a generator depending on whether the current flows in or out. (in other words within a simulation it's pretty easy to see what takes place)

--------------------------------------

Maybe this forum is not filled with technical people?

unime

Regeneration does not need to be implemented as a drag brake. There are ebikes out there that sense brake lever position and activate regeneration when the lever is first activated, but before the brake itself is engaged. I recall reading about one system with multiple level of regeneration operated this way.

There is very little downside to this type of regeneration when applied to a direct drive hub motor, but the benefit is limited by the efficiency of the motor (likely to be about 50% during acceleration and braking, for a net result of 25% energy return) and the charging current limit on the battery. Real world energy recovery is likey to be limited to single digit percentages (ignoring the use of cutting edge technologies like ultracapacitors).

Personally, I would rather have a bike that pedals freely - without having to overcome motor cogging torque - than regenerative braking. The regeneration systems I am familiar with use direct drive hub motors that are a drag when riding without power. Geared motors (hub or otherwise) typically freewheel and cannot be used with regeneration, but they have no cogging torque and their higher efficiency should make them competitive with most regenerative systems.

Because there are losses, the equations are not generally reversable. Operating as a motor, you have E_mechanical = E_electrical * efficiency, but as a generator the equation becomes E_mechanical = E_electrical/efficiency. If you want a more technically oriented discussion, check out the forums at endless sphere.

safe

I'm really not all that concerned with the efficiency of the generator at this point. In fact I think it's the obsession with the recapturing of the energy that gets people lost. (they miss the bigger picture)

The "point" is that people use the term "regen" thinking that it means that somehow you are recapturing energy that is "not being used" somehow. In some cases I can see hard braking before going into a turn as a valid argument for using an energy recapture system (like KERS in F1) but "regen" usage is best done in the middle of straight aways when you would otherwise be coasting freely.

"Regen" = "Regenerative Braking" (you don't get "free energy" it's going to slow you down)

But think of what people are being asked to do... they are being asked to use their "regen" on long downhills. The argument goes:

"Oh, I like going slow downhill... it's so relaxing."

(if that's one view of long distance riding that's not going to help promote ebiking to the general public that's for sure)

-------------------------------------------

What I seek to show is that in something like a Tour De France style race that the adoption of "regen" has absolutely no benefit and would actually cause the user of the technology to fall behind if they actually used it fully.

---------------------------------------------

As I said in a previous posting... if a rider slows himself with "regen" on a long downhill he has to make up that time somewhere else. This means that the rider using "regen" would need to use MORE energy on the flat land after the hill just to catch up with the pack. Add into it that on a downhill there are advantages to staying up with the pack because you can reduce aerodynamic losses by drafting.

--------------------------------------------

Sometimes there are things that are simply "not adequately challenged" and regen is one of them.

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Is the basic argument clear?

borland

pluses..

- For power assist configuration, the regenerative braking also captures some human effort that is expended going up hill. Not all, because of efficency losses.

- regenerative braking extends assisted pedal range, also having the effect of a lighter bike due to smaller battery requirement.

- regenerative braking reduces battery recharge times due to decreased battery consumption.

- regenerative braking reduces wear on conventional braking systems.

- On the BionX system, you can control the level of regeneration on the fly.

negatives ....

- regenerative braking can require increased maintenance, if it over time loosens the axle nuts due to counter axle torque.

- regenerative braking takes some getting used to.

safe

You forgot to mention that it's slower. It's regenerative "braking"... which means that you need to use it only when you would normally brake had you been on a freewheel configured bike. (otherwise you fall behind)

All the time you are slowing yourself down with the regenerative braking the guy with the freewheel right next to you is coasting ahead and leaving you far behind.

Don't we count in the idea of "performance" the idea that one wants to get somewhere?

The way people are thinking of regen they seem to factor out this "performance" line of thinking. It would never make much sense in a long distance race of ebike verses ebike because the other bike using a freewheel is more "efficient". (it's better at going fast)

If two ebikes start at point A, one has regen, the other has a freewheel, and they are otherwise identical, then the freewheel bike will always reach point B first after going over a hill even if the regen bike uses excess energy to try to catch up when on the flat.

The freewheel will always win...

--------------------------------

But I thank you for presenting the traditional arguments.

LesMcLuffAlot

"Regen" is not short for "regenerative braking." It is short for "regeneration." I'm thinking safe hasn't ridden a BionX system bike. You don't have to use the hand brake to engage the regeneration system. From the controller you can set it to "regen" mode and continue to pedal without engaging the brake lever. It has 4 different levels of "regen" resistance. This comes in handy on fast downhills, or strong tailwinds. You can continue to pedal while it is in this mode, and provides a small but sometimes significantly important boost in range. So your average speed may slow a small bit. That extra little bit of extended range could help someone ride up a monster climb that otherwise might have them pushing their bike near the end of their ride. I speak from personal experience.

Your in cycling, electric or otherwise,

LesMcLuffAlot

borland

You forget, the regenerative bike is faster and lighter, making it to the top of the hill first, leaving the non-regenerative bike with heavy battery far behind. So the rider has a much deserved resting period while he coast down hill in regenerative mode. Once reaching bottom of the hill, the rider is fully recharged, able to extend the lead even more.

I know from experience in gearing, closer matched gearing allows shifting down to more efficient pedal rate upon increased road grade. Wider spacing means dropping down more in term of speed, so closer gearing means faster recovery to top speed when road grade is restored.

misslexi

I'd agree with the OP, regen when invoked purely to recharge the batteries at the expense of the momentum gained by freewheeling is suspect. If it can be used in lieu of brakes that seems sensible.

unime

So regenerative braking is likely to make race cars go faster, but slows bicycles??? I don't think so. You have put forth a strawman argument by asserting that regeneration used on bicycles must be done inefficiently and is therefore inefficient.

[edited for better accuracy, using this bicycle calculator]
Now consider this time trial scenario. Descending a 1 mile hill, use regeneration to slow your descent from 30 mph down to 29. This add 4 seconds to your descent. On the following 1 mile ascent, despite inefficiencies you are able to use the stored energy to go 1 mph faster, increasing your speed from 5.6 to 6.6 mph, and thereby saving 97 seconds on the climb. The net result is 93 seconds faster, 12% off the original time.

There are clear advantages to the savvy use of regeneration and you better believe that competitors would jump at the chance to make use of it in a Tour de France style electric bike race.

safe

I think we are all at least becoming aware of the core equation that applies to regen now. I'm not talking about the efficiency equations (which are a totally separate issue) but the relationship of time and regen.

Regen (gained) = Time (lost)

...now the argument that somehow what is "gained" can be used later to erase what is "lost" is something worth exploring more. (that's a real and valid thing to consider)

If one recaptures energy on the downhill and uses that energy on the flat to catch up then the added aerodynamic drag (and the fact you have lost connection with the leaders) means you will give most of the energy back to the wind.

If instead someone recaptures the energy on the downhill and then simply stays far behind until the next hill climb then you would just catch the leaders when you used up your extra energy savings.

...there are other scenarios to ponder I'm sure, but the math doesn't look all that great for regen in a situation where time is important. (like in a race)

The argument for a smaller battery makes some sense... that's one to simulate and see what happens.

Regen is just fine if you are interested in a slow cruise... in fact one of the ironies of regen is that the SLOWER you make your trip the easier your trip will be. If you rode up the hill at 5 mph and then regeneratively braked down it at 5 mph then you would have the maximum energy recaptured.

Note: One mph out of 30 mph is different than 1 mph out of 7 mph. (on the climb) Basically I don't think that the numbers will work out that way. You need to actually create formulas that include the way electric motors work. Try those ideas again and use 0.5 mph on the climb and then you would probably be closer to the truth. You need to think in terms of energy recaptured by the motor verses energy required to run the motor. The losses are at least 50% in that exchange.

safe

KERS vs Regen

https://www.racecar-engineering.com/a...s-modular.html

Kinetic Energy Recovery Systems (KERS) do things very differently than regen on ebikes. The biggest difference is that ebikes use permanant magnet motors, but for something like F1 (or the Tesla Roadster) they use Induction motors that have the ability to efficiently handle high loads. This difference in scale (you need at least 1000 watts and above to do Induction motors efficiently) means that it's possible to do things in a F1 car that you can't do on an ebike.

KERS actually does make sense because it can capture a lot of energy at the exact time you need to... during hard braking.

Regen works best when the recapture rate is slow. So regen needs to operate as a sort of "dragging brake". Dragging the brakes will slow you down and that means you need to speed up later to compensate... so the tendency is to break even.

Both systems seek to recapture energy, KERS only works with hard braking.

safe

The Regen and the Freewheel... the Tortoise and the Hare?

unime

You can put an equal sign between those two terms, but that doesn't make it a valid equation. I have already given you two counterexamples: First, regeneration user to recover energy during necessary braking; and, second, strategic regeneration that allowing you to go faster by saving energy downhill, then using it uphill where the extra speed makes a bigger difference.

I'm sorry to tell you this, but your premise is fundamentally wrong.

In a serious ebike race, you would still ride in a pace line downhill, but you (and your team) would be recovering energy for use on the next climb. The time lost on the downhill section is easily made up by gains on the next climb, as I have already shown.

Didn't you read my last reply??? The math overwhelming supports the use of strategic regeneration - go back and check your work.

I don't think you are equipped to argue with my example. Work through it before arguing (use the energy calculator I linked and make reasonable assumptions). Come back and apologize for questioning my numbers when you are done. The reason you get a remarkable benefit is that the marginal drag when accelerating from 29 to 30mph is far higher than when going from 6 to 7. Also, increasing your minimum speed has far greater benefit on elapsed time than the cost of decreasing top speed by the same amount, so the net result is a big win, despite some significant inefficiency in regeneration.

By the way, I assumed the net result of regeneration was 25% energy recovery. If 100% of the energy were available, your uphill speed would be 4 mph faster in the example I gave. That would improve your time by almost 4 1/2 minutes in just 2 miles, but, alas, 100% efficiency is not possible.

-----------------------------

I have been making some assumption in defense of regeneration, and I don't mean to say that currently available systems are as good as I would hope. My chain driven ebike (without regeneration) is far more efficient at hill climbing than any hub motor, making it a better choice for just about any race I could imagine (assuming equivalent battery packs) than a hub motor with regen.

safe

"...strategic regeneration that allows you to go faster by saving energy downhill"

Before we go on we need to be clear what happens with "regenerative braking".

When you are at the top of a hill you have potential energy that if released using a freewheel allows you to use gravity to propel you forward.

"Regenerative Braking" always means you are GOING SLOWER down the hill than otherwise.

So before one ever gets a chance to "get ahead" with what you recover (which after a 50% loss on the recapture and other 30% loss when you use it again in the motor, plus battery losses) you have to catch up to where you would have been otherwise.

Do you understand the "negative speed" aspect of regen?

Regen, if used, makes a bike go slower... not using it means you coast faster down a hill...

------------------------------------

We have to get to this "baseline" before we go on.

Are we in agreement?

-----------------------------------

The "big realization" on this comparison is much like you inferred... we are ultimately comparing:

Losses due to aerodynamics (freewheel down a hill)

verses

Losses due to motor and battery (regen)

...the net gain or loss is entirely dependent on these factors. In most cases the two will more or less cancel each other out. However, I'm sure that one can do math to support whatever they want, but these are the dynamic forces at play.

-------------------------------------

If one loses 10 watthours in aerodynamic losses on a hill, but arrives at the bottom in one minute.

While another loses only 2 watthours in aerodynamic losses, arrives at the bottom in two minutes and recaptures 25% of the hills energy (let's say the hill has a potential of 100 watthours and so we recover 25 watthours)

Okay, so now the regen is one minute behind, so it has to work harder to get up the next hill...

The freewheel bike goes up at a rate that uses up 100 watthours.

The regen needs to catch up a minutes worth so it needs to use more than 100 watthours to catch up... whether it's 125 watthours or 150 watthours depends on the motor.

-------------------------

What if the race has a motor power limit to it? (after all, if it's an ebike it's going to be limited)

How does the motor catch up even if it had the energy available to it?

-------------------------

When you look at motors and how they behave as far as efficiency, it's very hard for a motor to use more power while still remaining efficient. The freewheel bike can use the motor more sparingly and efficiently because he has a huge lead. The regen bike needs to increase the power to catch up and that adds to the already bad efficiency situation.

--------------------------

Hey and it gets worse... don't forget about motor heating!

When you do regen it heats the motor as if it was climbing, so you are adding to the motor heat. The freewheel bike runs cooler and so it can be made lighter. The regen machine needs more thermal mass to deal with the added heating. Some of the hub motors weigh as much as 25 lbs. Hot motors also run less efficiently, so again it's another negative on top of a pile of other negatives.

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Ultimately we can get to the math, but I just want to get all the factors out in the open so that when it all comes together it's not coming as a total surprise. If I were to arrive at the end too quickly then people might be skeptical, but by going through everything first it will make conclusions make more sense.

safe

Using the online calculator: (go ahead and plug in values to prove to yourself it's true)

https://www.me.psu.edu/lamancusa/Prod...e/bikecalc.htm

Start with all the default values...



Downhill (5% negative slope for 10 miles)

Freewheel - 10 miles / 24.35 mph = 0.41 hours (net power gain/loss is zero)

Regen - 10 miles / 15.00 mph = 0.67 hours (behind by 0.26 hours)

Recaptured Energy = 0.133 hp * 746 watt = 99.22 watt

99.22 watt * 0.67 hours = 66.48 Wh * 0.7 (motor losses) = 46.5 Wh

46.5 Wh * 0.9 (battery losses) = 42 Wh (this is the energy recovered)



Uphill (5% positive slope for 10 miles)

Freewheel - 10 miles / 7 mph = 1.43 hours

Power Needed - 0.187 hp * 746 watt = 139.5 watt / 0.7 (motor losses) = 199.3 watt

199.3 watt * 1.43 hours = 285 Wh

Regen - Must do 10 miles in 1.43 hours - 0.26 hours = 1.17 hours

10 miles / 11.7 mph = 1.17 hours

Power Needed - 0.337 hp * 746 watt = 251.4 watt / 0.7 (motor losses) = 359.1 watt

359.1 watt * 1.17 hours = 420 Wh

...but we get to subtract the "savings" so the actual value is:

420 Wh - 42 Wh = 378 Wh



---------------------------------



Conclusion:

For the regen ebike to reach the second peak at the same time as the freewheel ebike it will use:

378 Wh - 285 Wh = 93 Wh more than the freewheel...


---------------------------------

Have I made any mistakes? (it's possible, mistakes are always possible)

.

unime

I'm sorry, but I can't completely make sense of your calculations. For one thing, multiplying watt hours and horespower gives power squared, a unit I have never encountered a use for. You also made a mistake calculating the speed needed by Regen to catch up with Freewheel.

Let's go over the scenario a little more carefully:

Downhill (5% negative slope for 10 miles)

Freewheel - 10 miles / 24.35 mph = 0.41 hours (net power gain/loss is zero)
Regen - 10 miles / 15.00 mph = 0.67 hours (behind by 0.26 hours)

So far so good. Now, let's use that energy calculator to save some work. It calculates -5.7 Calories (kcal) burned per mile (the minus sign means the energy is available for regen). Over 10 miles, that amounts to 57kcal (66 Wh, but there's no need to convert).

Using your estimates of efficiency (0.7 generator efficiency and 0.9 battery efficiency), that works out to 57*0.7*0.9 = 36 kcal of energy stored in the battery via regeneration, close enough to your figure of 42Wh to say they are the same. Excellent!

Uphill (5% positive slope for 10 miles)

Freewheel - 10 miles / 7 mph = 1.43 hours
Here's where out calculations start to differ. The calculator says it will take 170 kcal to complete this climb.

Regen needs to make up 0.26 hours, and finish in 1.17h. He'll have to travel at 8.5mph (10miles/1.17hours). Calculator says: 175 kcal - only 5kcal more than Freewheel, and we saved up 36 kcal. Assuming 70% efficiency, we end the climb even with Freewheel and with 29kcal left over. Not too shabby.

But, let's see what happens if we use up the 36kcal completely. After losing 30% due to inefficiencies, that's 25 kcal extra to spend on the climb, enabling Regen to zoom up the hill at 14.5 mph. Regen makes the climb in 0.69 hours, 0.74 hours faster than Freewheel's 1.43. Finish times are Freewheel: 1.84 hours, Regen: 1.36. A staggering defeat for Freewheel.

safe

You actually caught an error... yes... the speed to catch up is 8.5 mph and not 11.7 mph.

People in the ebike world tend to use Watthours because that's how we think of our batteries. Cyclists tend to use things like calories. I'm going to stay in the ebike world for my numbers if that's okay. Basically a watthour is just a watt applied for an hour, so it's easy when you are dealing with motor output that is normally in watts.

----------------------------------

Let's start to include things like the motor heating and the resulting inefficiencies that they might add to the problem. We do the calculations again (with the correction) and now we adjust the motor for higher heating and higher loads so that rather than 70% efficiency we use a figure like 60%. (which is pretty realistic for a motor asked to work 172.3 watt / 139.5 watt = 24% more power)



Downhill (5% negative slope for 10 miles)

Freewheel - 10 miles / 24.35 mph = 0.41 hours (net power gain/loss is zero)

Regen - 10 miles / 15.00 mph = 0.67 hours (behind by 0.26 hours)

Recaptured Energy = 0.133 hp * 746 watt = 99.22 watt

99.22 watt * 0.67 hours = 66.48 Wh * 0.7 (motor losses) = 46.5 Wh

46.5 Wh * 0.9 (battery losses) = 42 Wh (this is the energy recovered)



Uphill (5% positive slope for 10 miles)

Freewheel - 10 miles / 7 mph = 1.43 hours

Power Needed - 0.187 hp * 746 watt = 139.5 watt / 0.7 (motor losses) = 199.3 watt

199.3 watt * 1.43 hours = 285 Wh

Regen - Must do 10 miles in 1.43 hours - 0.26 hours = 1.17 hours

10 miles / 8.5 mph = 1.17 hours

Power Needed - 0.231 hp * 746 watt = 172.3 watt / 0.6 (motor losses) = 287.2 watt

246.2 watt * 1.17 hours = 336 Wh

...but we get to subtract the "savings" so the actual value is:

336 Wh - 42 Wh = 293 Wh


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So now they balance again.... slight advantage to the freewheel...


The truth is going to come down to the efficiency of the regen system. The better the efficiency the more likely that someone can break even or get ahead. The lower the efficiency the more certain that regen loses.


-----------------------------


Another factor is gears... are we to allow gears with regen? How does one implement it? We know that with a freewheel you can use multispeed gearing that's critical to getting your efficiency up higher.

So would we want to explore more "real" situations that involve actual hub motors using regen and compare them to multispeed freewheel bikes on the same track?

This is where I've gone with my simulation program (which I'm still tinkering with) in that it uses real motors and gives results about real things.


-----------------------------

In principle there is the potential for regen to make sense... but does it in practice?

How many one speeds have won the Tour De France lately? (hub motors are one speeds)

If you use a hub motor that is designed to go faster then it will tend to have lowered efficiency when climbing hills. Choose a slower top speed setup for your hub motor and hill climbing is better, downhill regen is good, but you are then restricted on the flat to slower speeds.

.

safe

Motor Efficiency Break Even Point

I took the numbers that we used in the last calculation and produced a chart that shows how motor efficency can completely negate any advantage that regen might deliver. If one attempts regen and ignores the value of proper gearing their chances of beating the bike with a freewheel (and multispeed gearing) is low. Real world riding needs to have sufficient gearing to cover differing slopes.

Depending on the rules of the race (and if we are talking about ebikes and not emotorcycles) we would likely have to deal with some restriction on power output or input for the motor too.

Anyway... this gives an idea of how critical efficiency is to this comparision.



.

safe

This would be the best case scenario... the motor would have to produce more than twice the power levels of the freewheel bike, which might either lower the efficiency or make the bike illegal as an ebike.

Which leads to the next topic...

safe

Setting The Rules

Let's set the rules as they would likely be set for an actual ebike race.

Maximum motor input 1000 watts. (output is up to the efficiency of the system and we will assume that it's 80% in all cases) Most everyone uses the same motor. We assume that gearing is always "perfect" whether you use a freewheel or not. (just to make things easier)

Battery size is whatever you want it to be for the race length and you can use whatever chemistry you want. Competition makes people seek the same things so the battery mostly cancels each other out.

So doing our numbers again:


Downhill (5% negative slope for 10 miles)

Freewheel - 10 miles / 24.35 mph = 0.41 hours (net power gain/loss is zero)

Regen - 10 miles / 15.00 mph = 0.67 hours (behind by 0.26 hours)

Recaptured Energy = 0.133 hp * 746 watt = 99.22 watt

99.22 watt * 0.67 hours = 66.48 Wh * 0.7 (motor losses) = 46.5 Wh

46.5 Wh * 0.9 (battery losses) = 42 Wh (this is the energy recovered)



Uphill (5% positive slope for 10 miles)

Freewheel - 10 miles / 24.8 mph = 0.40 hours

Power Needed - 1.340 hp * 746 watt = 1000 watt / 0.8 (motor losses) = 800 watt

800 watt * 0.40 hours = 320 Wh

Regen - Must do 10 miles in 0.40 hours - 0.26 hours = 0.14 hours (but it can't because it's an ebike)

10 miles / 24.8 mph = 0.40 hours

Power Needed - 1.340 hp * 746 watt = 1000 watt / 0.8 (motor losses) = 800 watt

800 watt * 0.40 hours = 320 Wh

...but we get to subtract the "savings" so the actual value is:

320 Wh - 42 Wh = 278 Wh

However we are still 0.26 hours behind. (but with a more full battery)

--------------------------

The problem that regen would have in an actual race situation (aside from the discussions about efficiency) is that if there is a power limit on the motors you can't make up time by using the extra power you had stored by going slow before on the downhill.

In such a scenario the freewheel easily wins, just because power and speed wins.

...what's to stop the freewheel (or the regen system) from just going fast everywhere and never letting the tortoise catch up?

(if the battery is large enough why not just hold the throttle wide open all the time)

unime

Safe, I don't know how to say this more clearly but you are wrong, flat wrong, plain wrong, simply wrong, and almost completely wrong. I've shown you your mistakes and will show you new ones as they arrive. I also think you have a lot of gall, saying my calculations don't feel right without working through them yourself to see I have made no error.

Tell me, why do you insist in repeatedly coming back with your bad assumptions and incorrect calculations? This time, the first mistake I caught was dividing by 0.7 to account for generator inefficiency, instead of multiplying. I stopped there, because I have given you all the information you need to get it right. Please check my calculations before suggesting new scenarios as an attempt at refutation. You will find my work is correct (to within a significant figure or two). Think ... carefully ... about what we have been discussion before coming back with more bad conclusions derived from faulty logic.

By the way, PLEASE use correct units if you are going to bother writing them. I was mislead by your use of the term "746 watt", where you should have had "746 watt/HP". Also, I hardly need a lecture on the use of appropriate units. As I explained, expressing energy in kilocalories simplified my presentation because that is the unit the bicycle calculator presents as its result. I even showed you the conversion to watt hours the first time I used the unit, to help eliminate any possibility of confusion. Apparently to no avail. Maybe next time I'll present my calculations in the FFF system of units in protest of your pickiness.

There are several solution to this problem. An internally geared (ala rohloff's speedub) hub motor could be possible, as could a secondary chain driving the motor through a completely separate path when using regeneration. The simplest solution might be fitting the bike with a separate generator (say, a small, high efficiency outrunner) driven directly by friction on the wheel and disconnected when not in use. Perhaps you can think of some solutions if you try.

No, no, no! Not until you are able to understand the simple case.

----------------

Regarding your "real world" race scenario. You suggest a strategy that leaves some charge in the battery at the end of the race. That's simply a bad strategy. No rational competitor will choose to end the race with charge left in the battery. For short races with limits on motor wattage, it probably pays to load up with enough battery to run flat out the whole way.

Last, please understand I bear you no ill will. One of the things I get a personal reward from is tutoring people in math and physics, as I am trying to do here. I very much enjoy applying physics to athletic activities like cycling, so this topic is right up my alley. However, I can only help you if you are willing to listen.

safe

Our Math Agrees...

You are having trouble with how I presented the math... but the math is correct because our results are in agreement. I divide by losses in order to work backwards to how much actual battery energy is required to create the power needed.

Let's review using your scenario:



Downhill (5% negative slope for 10 miles)

Freewheel - 10 miles / 24.35 mph = 0.41 hours (net power gain/loss is zero)

Regen - 10 miles / 15.00 mph = 0.67 hours (behind by 0.26 hours)

Recaptured Energy = 0.133 hp * 746 watt/hp = 99.22 watt

99.22 watt * 0.67 hours = 66.48 Wh * 0.7 (motor losses) = 46.5 Wh

46.5 Wh * 0.9 (battery losses) = 42 Wh (this is the energy recovered)



Uphill (5% positive slope for 10 miles)

Freewheel - 10 miles / 7 mph = 1.43 hours

Power Needed - 0.187 hp * 746 watt/hp = 139.5 watt / 0.7 (motor losses) = 199.3 watt

199.3 watt * 1.43 hours = 285 Wh

Regen - Must do 10 miles in 1.43 hours - 0.26 hours = 1.17 hours (or less)

10 miles / 14.5 mph = 0.69 hours (which bets the freewheel)

Power Needed - 0.443 hp * 746 watt/hp = 330.5 watt / 0.7 (motor losses) = 472 watt

472 watt * 0.69 hours = 326 Wh

...but we get to subtract the "savings" so the actual value is:

326 Wh - 42 Wh = 284 Wh


----------------------------



But my point was that you are forced to increase the power level by a factor of:


0.443 hp / 0.187 hp = 2.36 = 236% the power output.


In many cases when you are forced to run at a higher power level you lose efficiency and that's what made the issues that followed after it apply.

.

safe

The Differing Battery Size Scenario


What if we vary the battery size?

Freewheel pack is set at 30 lbs (so change the online calc to read 150 total lbs)

Regen pack is set at 15 lbs (so change the online calc to read 135 total lbs)

The freewheel pack has 800 Wh.

The regen pack has 400 Wh.

Now we do the calculations again:




Downhill (5% negative slope for 10 miles)

Freewheel - 10 miles / 26.8 mph = 0.37 hours (net power gain/loss is zero)

Regen - 10 miles / 15.00 mph = 0.67 hours (behind by 0.30 hours)

Recaptured Energy = 0.156 hp * 746 watt/hp = 116.4 watt

116.4 watt * 0.67 hours = 78 Wh * 0.7 (motor losses) = 54.6 Wh

54.6 Wh * 0.9 (battery losses) = 49 Wh (this is the energy recovered)



Uphill (5% positive slope for 10 miles)

Freewheel - 10 miles / 13.5 mph = 0.74 hours

Power Needed - 0.476 hp * 746 watt/hp = 355 watt / 0.7 (motor losses) = 507 watt

507 watt * 0.74 hours = 376 Wh

Regen - Must do 10 miles in 0.74 hours - 0.30 hours = 0.44 hours (or less)

10 miles / 22.94 mph = 0.44 hours

Maximum input power - 0.938 hp * 746 watt/hp = 700 watt / 0.7 (motor losses) = 1000 watt

1000 watt * 0.44 hours = 440 Wh

...but we get to subtract the "savings" so the actual value is:

440 Wh - 49 Wh = 391 Wh


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But what happened to all the regen savings we were hoping for?

If the motor is limited in power (1000 watts input) then the regen bike will go as fast as is possible to catch up. If the freewheel bike goes just fast enough to stay ahead of the regen bike then it only uses as much as is needed to win.

It's a "reverse calculation" to do... the freewheel "Hare" gets to be lazy only going as fast as it needs to be. The regen bikes motor gets "maxed out" and can't catch the "Hare" because the "Hare" can use up more energy if it needs to. (after all it has a battery twice the size)

Not only that, but the freewheel bike has a pack with double the energy so we got to the end of the race and the weight difference didn't help the regen bike very much.

Freewheel - 800 Wh pack and uses 376 Wh = 53% in reserve.

Regen - 400 Wh pack and uses 391 Wh = 2% in reserve.

.

cerewa

This conversation is amusing. Taking facts that are situation-dependent and are part of highly complex systems, simplifying, and then making conclusions as though they were absolute truth for all realistic situations.