Elite vs Platinum-does the 20mph speed limiter conserve battery?

[Brambor]

This might be a dumb question but I thought I would ask anyway: If I bought the larger battery upgrade for the Stromer Elite and then tried to compare battery consumption between Elite and Platinum for identical commute, would the Elite have more battery left at the end of the day due to the speed limiter?

 

[Admin]

Hey Brambor, there's no such thing as a dumb question here so no worries! Also, I just fixed your title - thanks for pointing it out

This is actually a very interesting and potentially complex question. It makes me think about cars which tend to get their best gas mileage at ~50 miles per hour. I did some research and found an interesting statement put out by fueleconomy.gov as follows:

While each vehicle reaches its optimal fuel economy at a different speed (or range of speeds), gas mileage usually decreases rapidly at speeds above 50 mph. You can assume that each 5 mph you drive over 50 mph is like paying an additional $0.24 per gallon for gas.

So that part about "or range of speeds" seems to indicate that each gear on the car has an optimal speed which is leveraging the most natural and efficient RPM (rotations per minute) of the motor. This is not as true with electric motors and there are differences between geared and gearless designs but let's just assume there is an "optimal" output for them as well.

The other big factors to consider are aerodynamics, drag and speed. A Toyota Prius is much more aerodynamic than a Toyota 4Runner which is much more aerodynamic than a typical person riding a bicycle... Yep, you read that right! Even though a person on a bike is much smaller than a car, most cars produce way less drag. We're like big flat sticks with no windshields or curved edges or spoilers to direct airflow... unless you're on a recumbent bike and that makes a big difference, especially at higher speeds.

I found some stats at this website that explain how a recumbent bicycle is much more efficient than an upright bike, especially with a front and rear fairing (windshield). On an upright bike at 12mph, half of the energy you spend pedaling goes towards internal mechanical friction and the rest goes into fighting air resistance. At 25mph however, about 85% of your pedaling energy goes into overcoming air resistance. On a fully faired competition recumbent at 25 miles per hour, less than 25% of your pedaling energy is used in overcoming air resistance! The recumbent isn't necessarily faster for this saving in efficiency, but it is easier to keep going for longer distances (which equates to saving energy in a battery pack) this is part of what makes the Outrider 422 Alpha recumbent ebike so cool and efficient!

So wind resistance increases as speed increases, basically more of your energy goes towards "pushing air" and this means you get tired or run your battery out faster. Here's some more science from a guy at this forum talking about motorcycles vs. cars and note that motorcycles have slick sides, windshields etc. vs. a bike that is usually completely exposed.

Total drag (Dt) and drag coefficient (Cd) are two completely different but related things. Cd is equal to the coefficient of parasitic drag (Cdp) plus the coefficient of induced drag (Cdi). Cdi is minimal on motorcycles though so it can be effectively disregarded.

Total drag (in lbs) can be found by multipyling the Cd, dynamic pressure* (q), and surface area (S).

* dynamic pressure is made up from the density ratio (local air density accounting for local altitude, temperature, and barometric pressure measured against standard density) multiplied by the air velocity in knots squared. The resultant of that is then divided by 295.

The formula looks like this: Dt=Cd(q)S

As you can see, drag is determined by five factors. Cd, surface area, local pressure, local temperature, and air speed.

High end sports cars generally have Cd numbers in the mid 0.3s. Motorcycles however have Cd numbers close to 1.0 depending on the model bike, size of rider, and riding position. In looking at the formula you should be able to deduce one major point. Drag increases exponentially with speed (unless the wind is blowing really hard in the same direction you are riding). Plugging in some generic numbers helps to demonstrate this.

Variables: Standard atmosphere (sea level, 15 degree C, and a barometer of 29.92), Car at .35 Cd. Bike at 1.0 Cd. Car surface area at 19 sq. ft. Bike surface area at 7 sq. ft. (surface areas and Cds are approximate numbers).

50 kts

• Bike Dt = 59.32 lbs
• Car Dt = 56.35 lbs

100 kts:

• Bike Dt = 237.3 lbs
• Car Dt = 225.44 lbs

150 kts:

• Bike Dt = 533.90 lbs
• Car Dt = 507.20 lbs

Conclusion:

In the case of cars vs. motorcycles, the bikes generally have triple the Cd but 1/3 the surface area so Dt remains about the same regardless of speed. Cars kick the crap out of bikes at high speeds because at high speeds the predominant factor is aerodynamics. As speeds increase the rate of acceleration decreases and the superior HP/weight ratio that gave the bike superior acceleration at low drag speeds cease to be the deciding factor. At high speeds where rates of acceleration are minimal you need horsepower to overcome the drag factors. As we have seen, aerodynamic drag is approximately equal so whoever has the most horsepower wins.

I did a bit more research on the coefficient of drag on bicycle riders and found the following stats at this site which support the quote above. We are about ~1.0 Cd which is what the motorcycle was in his example. Note that the bullets below vary between different handle bar setups and that is in large part due to body position, the further you're bent forward the smaller the forward surface area is and thus, drag is reduced:

• Wing or Teardrop: 0.005
• Ball: 0.5
• Person standing upright: 1.0
• Flat plate face-on to airflow: 1.17
• Brick: 2.0
• Cyclist (regular bars)*: 1.15
• Cyclist (hooded bars)*: 1.0
• Cyclist (drop bars): 0.88
• Cyclist (aero Bars): 0.70

So anyway, I think it all boils down to this: "Aerodynamic drag increases with the square of speed; therefore it becomes critically important at higher speeds." regardless of motor efficiency, you're going to encounter more drag at higher speeds and for this reason and the fact that people on bikes (who aren't wearing triathlon helmets) are already producing a lot of drag, I'd say yes! The 20 mph speed cap on the Elite is going to extend the range... but I don't think that's why they did it and the energy saved will likely be negligible.

The other part of your question mentioned battery sizes but if I understood correctly you'd be upgrading so both packs would be the same. The big difference is top speed right? So yeah, if you use more of the battery fighting the wind at higher speed because we aren't very aerodynamic and drag increases with the square of speed... then yep, you'll use the battery quicker

Yay for learning! ps. the drag coefficient of a Toyota Prius is 0.26 and the drag coefficient of a Toyota 4Runner is about .36 and again, a person on a bike is ~1.00

 

[Juerg]

That's a great explanation, Court!
It accords with my experience on a ride From North Vancouver (BC) up to Whistler.

Jamie and I we did that 110km (68 Mile) trip all in POWER mode with the 14.5Ah Battery, he on the ST1 Platinum and I on the ST1 Elite. With the Elite I did 70 km (43.5 Miles) on the first section a little bit further then Squamish and with the Platinum Jamie did 60 km (37.3 Miles). This section is up and down but the start and end are both on see level.

From Squamish up to Whistler we had to climb 2,200 ft on a distance of 50 km (31 Miles). on the Elite I needed a second battery and on the Platinum Jamie needed a second and 50% of a third battery.

Jamie made the whole trip on the Platinum in 3 hours and 45 minutes and I had on the Elite 4 hours and 5 minutes.

We both are sporty riders so we pushed the pedals really hard. If you're riding moderate you will get a bit more out of one charge.

This is a good example that the Elite gives you 10-20% more range on one charge but on the other hand the Elite has his speed limit reached at ~38km/h (~24 Miles) when the recuperation kicks in while you can go faster on the Platinum, that shortens your commute about 10-20%.

We will do the same test on ECO mode later this year when it's getting warmer.

 

[Brambor]

wow. outstanding example. Thanks Juerg. Were you and Jamie comparable weight?

 

[Juerg]

I'm 165lb and Jamie is about 10% heavier then me.

 

[James]

Hey Juerg I'm down to ride with you guys next time you go up! Let me know, maybe I can make it happen

 

[Juerg]

OK! We let you know.

 

[Admin]

The other day calvin shared this great resource on frames, drives, gears, wheels, steering, braking and aerodynamics. Wanted to tack it on here for reference http://www.exploratorium.edu/cycling/wheel3.html