I’ve seen scooters and cycles claiming 200 Watts and 18 mph prime pace and others claiming 400 Watts and 12 mph prime pace. How a lot energy does it really take to maneuver an individual round on an el scooter test or cycle? Bicycles, scooters, and even vehicles are all ruled by the identical elementary energy necessities. At fixed pace, the facility required to maneuver the car and the passenger goes to 3 locations:
- The facility required to beat the rolling resistance of the wheels on the pavement.
- The facility required to beat the wind resistance related to shifting the car/passenger by way of the air.
- The facility required/supplied to maneuver the car and passenger up/down any incline (if not touring on flat pavement).
We are able to write this as an equation:
Whole-Energy = Energy-rolling-resistance + Energy-wind-resistance + Energy-hill-climbing
(Observe that Whole-power is the facility delivered to the driving wheel of the car internet of any friction within the transmission and inefficiencies within the energy system.)
To a primary approximation, power-rolling-resistance is in flip decided by the load of the car/passenger (W), the pace of the car (S), and a coefficient that characterizes the rolling resistance of the wheel (a). Energy-rolling-resistance = aWS
To a primary approximation, Energy-wind-resistance is set by the “frontal space” (F) of the car/passenger (the realm of the define of the car/passenger when seen from the entrance), a coefficient (b) that characterizes the form of the car/passenger, and the CUBE of the pace (S x S x S).
Energy-wind-resistance = bFS^three
Energy-hill-climbing is set by the grade of the hill (G), the load of the car/passenger (W), the pace (S) of the car/passenger. Energy-hill-climbing = GWS
So, your complete equation is: Whole-Energy = aWS + bFS^three + GWS = (a+G)WS + bFS^three
Earlier than we do some calculations, we are able to make some attention-grabbing observations:
- Whole energy required is strongly influenced by pace.
- At excessive speeds, the impact of wind resistance shall be very massive (as a result of it is dependent upon S cubed).
- Gentle autos/passengers have an general benefit. In reality, though W doesn’t seem within the expression for wind resistance, frontal space (F) is extremely correlated with W, so general measurement/weight just about influences all three classes of energy consumption.
Now, some approximate numbers. (I exploit metric items, however present some examples and conversion components for these of you who assume in English items.)
- a = coefficient of rolling resistance
- zero.zero08 for a high-pressure 700mm highway bike tire
- zero.020 for a mountain bike tire
- zero.040 for a typical (e.g., 9 inch) pneumatic scooter tire
- W is weight in Newtons (1 pound = four.45 Newtons)
- S is pace in Meters/Second (1 mph = zero.45 meters/second)
- b = drag consider kg/m^three
- zero.6 for a square-edged field
- zero.four for many human-like shapes
- zero.2 for a egg-shaped object
- F = frontal space in sq. meters
- zero.four for a crouched racing bicycle owner and bicycle
- zero.6 for an upright bicycle owner and bicycle
- zero.eight for a standing scooter rider
- G = peak of climb/distance of climb (e.g., % grade)
- Typical most railroad grade = zero.02
- Typical most bike path grade = zero.05
- Typical most overpass grade = zero.08
- Most grade on Pike’s Peak mountain highway = zero.10
- Powell St. in San Francisco (cable vehicles) = zero.17
- How a lot energy is consumed to propel a medium-sized (165 lb.) grownup standing on a scooter with 9 inch pneumatic tires touring at 12 mph?
- W = 165 lb. = 734 Newtons
- S = 12 mph = 5.four Meters/second
- a = zero.040
- b = zero.four
- F = zero.eight sq. meters
- G = zero
Whole-Energy = (a+G)WS + bFS^three = (zero.04+zero)734 x 5.four + zero.four x zero.eight x 5.four x 5.four x 5.four = 159 + 49 = 208 watts