Quote:
Originally Posted by redyaris
A Cd of 0.38 for production a car is poor. My Yaris is at 0.29 in stock configuration and as modified it may be as low as 0.26 the same as a Prius. The honda insight is at 0.25. For your home work, answer this; if it takes 600 hp to push the car like a mustang with a Cd of 0.38 to 200mph how much HP would it take to push a car like the honda insight with Cd of 0.25 to 200mph? you may only use information from this website.
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Given we actually used the powertrain out of an insight (the original 3 cylinder ima insight, not the new one) in one or several of my automotive powertrain courses to power other theoretical range extended electric vehicles I happen to already have some of this information, however it is not difficult to calculate if you plug the numbers into the equations I provided.
The insight weighs 848kg empty with a/c a full tank of gas, and a 5-speed manual transmission, now assuming a minimal load of just a 150 lb/ 68kg driver the car would then weigh in at 916 kg.
Density of air is considered a constant for the range of speeds we would be considering, as the air flow is still sub sonic, and therefore the density used is 1.225 kg/m^3
The frontal area is 1.84 m^2 using 80% of the height and width information made available to me.
200 mph is approximately 322 kph, which works out to 89.44 m/s
On level pavement the road load force to over come the combination of rolling resistance and aerodynamic drag (this is the best case scenario, adding in any minor grade resistance and the power required to maintain this speed increases substantially
plugging in these numbers into the earlier equation, after converting units to their proper format the road load force is approximately 2295.0 N, to calculate the road load power required this is multiplied by the speed the vehicle is traveling, 89.44 m/s and gives a required road load power of 204 kW. 1 Horsepower is equal to 746 watts or 0.746 kW so to determine the road load power required one must divide 204 over 0.746 hp/kW. Therefore the required road load power is 273.5 at the wheels.
Now assuming a theoretical driveline with only a 10% loss (eta/efficiency= 0.9) from the engine to the wheels an insight would require the road load power divided by the efficiency (Prl/eta) 273.5/0.9 or 304 hp at the crankshaft in order to power an insight to this speed, this assumes you can package enough gearing/ engine within the original weight constraints of a gen 1 insight
However if the driveline is only 80% efficient the power required from the engine in order to go this speed increases to 342 horsepower ( a driveline loss of 20%)
Of course an actual insight capable of traveling at 200 mph while weighing around the same as stock seems unlikely.
On a counter point though, according to car and driver the 2011 Mustang GT500 only had a drag coefficient of 0.36, not 0.38, and I guess I shouldn't trust the online calculators, but instead run the numbers through my own matlab script that solves the equations correctly.
The GT500 would require only 343.8 kW to over come the road load force on level pavement at 200 mph, that works out to just 460.9 horsepower at the wheels, also assuming a 150 lb/68 kg driver. This means that for a driveline loss of just 10% the power required by the engine on level pavement is 512 hp or 382 kW. Would it benefit from being more streamlined, yes it could get away with less power on level pavement, I'm using the current mustang information as I am unable to get a hold of the information for the 2013 but I anticipate it to be roughly similar.
Again if the driveline were only 80% efficient in translating the power from the engine to the wheels the Mustang would require 429.75 kW or 576 hp, still shy of the 650 the engine is capable of cranking out, however the supercharger is stealing some power in order to run itself, however that should be accounted for in the resultant power from the crankshaft.