Influence of hills on range

[johrhoj]

I wondered: is there a simple calculation that can predict my range from the next properties: My weight (wheel included), battery size, and the hilliness of the route I am about to go.

Roughly said, your hilly range is your normal flat range minus 75 meter for every meter up and down. 

Since most of you know your flat range, this will do. But I also came up with a formula for your flat range (from real world experience myself and other people on this forum):

     10 km per 150 Wh (weight 75 kg)
     10 km per 175 Wh (weight 125 kg)

In a formula, with B = battery size in Wh and W = weight in kg, flat range is: 

     10.000 * (B / (150  + (W-75)/2) ) 

Example: you weight 87.5 kg and your Ninebot One E+ has 340Wh battery. So W=100 B=340. You go on a 15 km ride with 400 m up and down worth of hills. Will you make it all the way?

     flat range= 10000 * (340 / (150 + 12.5) ) = 10000 * 2.092 = 20920 m
     hilly range in this case is 3 km shorter (75 * 400), so you will make it. 

[esaj]

21 minutes ago, johrhoj said:

I wondered: is there a simple calculation that can predict my range from the next properties: My weight (wheel included), battery size, and the hilliness of the route I am about to go.

Roughly said, your hilly range is your normal flat range minus 75 meter for every meter up and down. 

Since most of you know your flat range, this will do. But I also came up with a formula for your flat range (from real world experience myself and other people on this forum):

     10 km per 150 Wh (weight 75 kg)
     10 km per 175 Wh (weight 125 kg)

In a formula, with B = battery size in Wh and W = weight in kg, flat range is: 

     10.000 * (B / (150  + (W-75)/2) ) 

Example: you weight 87.5 kg and your Ninebot One E+ has 340Wh battery. So W=100 B=340. You go on a 15 km ride with 400 m up and down worth of hills. Will you make it all the way?

     flat range= 10000 * (340 / (150 + 12.5) ) = 10000 * 2.092 = 20920 m
     hilly range in this case is 3 km shorter (75 * 400), so you will make it. 

This might give good rule of thumb-values, but unfortunately it won't work with all wheels, conditions, battery configurations & rider weights. Head/tail-wind alone can cause huge difference. For example, when @Tilmann made runs with headwind and tailwind at an empty airport runway, running against headwind needed 779W (watts, not watthours) of power on average at an average speed of little under 21km/h, and with tailwind, the average power was 399W with an average speed of almost 34km/h! Well, the values might not be correct knowing the inflated speed / current values reported by MSuper 2, but the ratio is probably close to reality (2x more power needed against headwind with about 1.5 times slower speed).

On top of that, the batteries will give out less total charge when higher discharge currents (more power) are used, as more of the power gets burned off as heat in the batteries themselves (voltage drop caused by internal resistance times current).

Personally, my "consumption" has been between 10Wh per km (100Wh per 10km) and about 14Wh per km (140Wh per 10km), depending on wind and temperature (same routes, similar ridestyles) on 264Wh 16S2P.

 

[johrhoj]

1 minute ago, esaj said:

This might give good rule of thumb-values, but unfortunately it won't work with all wheels, battery configurations & rider weights. Head/tail-wind alone can cause huge difference. For example, when @Tilmann made runs with headwind and tailwind at an empty airport runway, running against headwind used 779W (watts, not watthours) on average at an average speed of little under 21km/h, and with tailwind, the power usage was 399W with an average speed of almost 34km/h!

On top of that, the batteries will give out less total charge when higher discharge currents (more power) is used, as more of the power gets burned off as heat in the batteries themselves.

You are right on all points I guess (as usual  ). Like I said, if you know your normal flat range, than all you need is the 75m range loss per height difference. 

If you then know the loss of range due to bad circumstances (wind, gravel, etc.), say 80% of "normal flat range", then I think it will also be 80% of your "hilly range". Be adviced that if you have tailwind half the distance and headwind the other half, it will still shorten you normal range, because the headwind loss is greater than the tailwind gain. 

Your last points suggest that when you go steep hills, or hills with top speed, the range loss may be more than 75 m per vertical meter, because of maxing out power usage. If this is your riding style, maybe use 100m loss in stead of 75 meter loss, to be on the safe side. 

As you indicated, it is just a rule of thumb. Everyones experience with their own wheels (and riding style etc.), will teach them how far under/over this rule they are. 

[Ponne]

I ride a IPS zero 240Wh. i use it mostly for commuting. On the way from home to work i have only 20% left and on windy days i ride it almost complete empty. The ride is 7.5 Km in total and i climb 30 meter. with two steeper parts near the end. Most of the time i endure headwind.

On my way back i only need 50% capacity for the same trip. My weight inclusive backpack is almost 100Kg

[johrhoj]

10 hours ago, Ponne said:

I ride a IPS zero 240Wh. i use it mostly for commuting. On the way from home to work i have only 20% left and on windy days i ride it almost complete empty. The ride is 7.5 Km in total and i climb 30 meter. with two steeper parts near the end. Most of the time i endure headwind.

On my way back i only need 50% capacity for the same trip. My weight inclusive backpack is almost 100Kg

This seems pretty good fitting the rule of thumb.

You use 0.8 + 0.5 times your battery for a total of 1.3 * 240 = 312 Wh.
With you weight that would be about 19 km of flat range. With the 30m climb and descent that would be diminished with 30 * 75 = 2250m, leaving you a hilly route range of 16.750km. You said you did 15. The rule of thumb is 12% off.

Windiness is obviously a serious range cutter in your case. Do you have headwind in both directions? Or do you see a 60% left in stead of 50% left with tailwind?
Also did you include the weight of you wheel?

Thank you for this input

 

[Keith]

The problem is speed, including windspeed, consumes power exponentially as it increases, so the rule will vary significantly depending how fast you and your wheel are going. This cycling site: http://www.americanroadcycling.org/articles/PSL/WiddersHump/WattsSpeed.htm?frm=bkmrkImg2OrgFirthMalcomChart#02/11/08 has some interesting graphs of the effect of both rider weight and speed on power consumption. Looking at the speed graph it shows  100W at 16MPH, 200W only gets you to 21MPH.

Interestingly enough, another graph shows the effect of body weight has far greater impact the faster you are going,

The idea is sound, however I suspect each rider will need to do some measurements themselves to get the factors that apply to them. Interestingly I did a 9.86 mile run with an 80ft climb and descent in 60.2 minutes yesterday and I'm just recharging the wheel now with a Charge Doctor to see how much capacity I used.

Update

Recharging took 200.3Wh so pretty much an average consumption of 200W at an average speed of 9.86MPH (roughly 16k/H) max speed 15.5MPH (25k/h) that works out as 10km per 125Wh I'm 71kg without clothes etc.

[Ponne]

7 hours ago, johrhoj said:

This seems pretty good fitting the rule of thumb.

You use 0.8 + 0.5 times your battery for a total of 1.3 * 240 = 312 Wh.
With you weight that would be about 19 km of flat range. With the 30m climb and descent that would be diminished with 30 * 75 = 2250m, leaving you a hilly route range of 16.750km. You said you did 15. The rule of thumb is 12% off.

Windiness is obviously a serious range cutter in your case. Do you have headwind in both directions? Or do you see a 60% left in stead of 50% left with tailwind?
Also did you include the weight of you wheel?

Thank you for this input

 

I have misled you with the range. I forgot to tell that i need to recharge the wheel at work. After 7.5 Km with headwind and steady going uphill (30m level difference) the battery is flat; But when going back downhill with tailwind most of the time i have about 45% left.

I didnt count the weight of the wheel so that is another 11Kg extra.

[johrhoj]

Seems you have a very efficient wheel and/or riding style  

6 hours ago, Keith said:

The problem is speed, including windspeed, consumes power exponentially as it increases, so the rule will vary significantly depending how fast you and your wheel are going.

Actually friction against air increases quadratically with speed. So if you go from 16 to 21 (a factor 1.31 quicker), you have 1.72 times the air friction. Because of this, speed is the most influential factor on the range you go with one charge. With many wheels and users, I estimate the average speed lies around 15 km/h (traveling of course, not doing tricks).

 

6 hours ago, Keith said:

The idea is sound, however I suspect each rider will need to do some measurements themselves to get the factors that apply to them. Interestingly I did a 9.86 mile run with an 80ft climb and descent in 60.2 minutes yesterday and I'm just recharging the wheel now with a Charge Doctor to see how much capacity I used.

I totally agree. And I thank you for sharing this information.

 

6 hours ago, Keith said:

Recharging took 200.3Wh so pretty much an average consumption of 200W at an average speed of 9.86MPH (roughly 16k/H) max speed 15.5MPH (25k/h) that works out as 10km per 125Wh I'm 71kg without clothes etc.

What you put into the battery, you do not fully get out again. Li-Ion batteries are among the most efficient batteries, but I do not know what the loss is. Nor do I know if the Wh spec of the battery specifies what you get out of it, or what you put into it. I would guess the former. In any case, it means that you used even less energy to do your trip  

I very much liked the article behind the link you mentioned. Only for some part I think that the figures apply to both bicycles and EUC's. Bikes will have more mechanical friction and the bicyclist moves a lot of mass around (his/her legs). On the other hand the EUC already uses energy while standing still, and looses energy in the power supply itself.