3 ms·
I am a little skeptical that air resistance is a huge factor for an 80,000 pound fully loaded semi. Probably most friction losses are due to rolling resistance
by zackmorris 13y ago
I am a little skeptical that air resistance is a huge factor for an 80,000 pound fully loaded semi. Probably most friction losses are due to rolling resistance. As it’s a sunday and I’m daydreaming anyway, I might as well try some back of the napkin calculations:
http://www.engineeringtoolbox.com/drag-coefficient-d_627.html http://www.engineeringtoolbox.com/drag-coefficient-d_627.htm...
http://www.engineeringtoolbox.com/rolling-friction-resistance-d_1303.html http://www.engineeringtoolbox.com/rolling-friction-resistanc...
https://en.wikipedia.org/wiki/Semi-trailer_truck https://en.wikipedia.org/wiki/Semi-trailer_truck
Before I start, I don’t know if the Engineering Toolbox answer is wrong, because I get 217.5 N for (0.29 * 0.5 * 1.2 * ((90 * 1000)/3600)^2) * 2. At least it’s close to the 181 N they claim. So my results could be off but I’m hopeful they’re within the correct order of magnitude..
If we assume a drag coefficient of 1 for a flat plate representing the front of the truck, with most losses coming from form drag, A semi with a frontal area of 2.5x4 meters at 105 km/hr (65 mph or 29 m/s) would feel a force of:
Fd = 1.0 1/2 (1.2 kg/m3) ((105 km/h) (1000 m/km) / (3600 s/h))2 (10 m2) = 5104 N = 520 kg = 1147 lb
If we assume the high drag coefficient of 0.01 for truck tires, the rolling resistance of a 36287 kg (80000 lb) truck (idealized as independent of velocity) is:
Fr = 0.01 (36287 kg) (9.81 m/s2) = 3560 N = 363 kg = 800 lb
Power P = F * v so these are:
Air resistance power = 520 * 29 = 15080 W = 20.22 hp
Rolling resistance power = 363 * 29 = 10527 W = 14.12 hp
So on flat ground, amazingly it only takes about 26.1 kW (35 hp) to keep a semi moving at 105 km/hr (65 mph)! This makes sense to me because a human can pull a semi at about 5 mph. Power goes up roughly by the square of velocity so a human with a power of 300 W would need 13 * 13 = 50.7 kW (68 hp) to go 65 mph. We’ve seen here that roughly half the power goes to rolling resistance which stays roughly constant with velocity, so 35 hp is conceivable.
As a sanity check, climbing a 5% grade at 105 km/h is a climb rate of 5.25 km/h or 1.46 m/s. The power required to lift the mass of the truck is:
Power P = F * v = m * g * v = 36287 * 9.8 * 1.46 = 519194 W = 696 hp
So it takes toughly 20 times more power to go up a 5% grade, and that’s why a typical semi truck engine with 600 hp can’t climb a 5% grade at 65 mph.
Semi trucks get 5.5 miles per gallon, so use about 12 gallons per hour. There are 38 kWh of energy in a gallon of diesel fuel, so that’s 456 kW burned in an hour, or a continuous power used of 456 kW (612 hp). If we compare that to the ideal of 35 hp needed, we can see that:
Engine to road efficiency of a semi truck = 26.1 kW/456 kw (or 35 hp/612 hp) = 5.7%
That’s really quite remarkably low and doesn’t surprise me, since semi truck technology has not changed much in 50 years. I read somewhere that cars are in the 8-15% efficiency range. That’s why it’s so trivial for Tesla to beat an internal combustion engine, because electric motors are 95% efficient vs. about 25% efficient for an internal combustion engine.
So the real increase in efficiency of a hybrid gas turbine/electric semi comes from the turbine, which has an efficiency of 40% vs about 25 or 30% for a reciprocating diesel engine. Improved aerodynamics and decreased rolling resistance of a carbon fiber trailer are mostly for show. Hybrid turbine/electric propulsion has been used on trains for decades and I’m kind of flabbergasted why it never took off in semis, or cars for that matter.
- GFK_of_xmaspast 13y agoHaven't you noticed over the last 15 years or so that big trucks nowadays basically all have those cowls on top and they're a lot more rounded on the front.
- Tuna-Fish 13y agoTurbine systems scale up in efficiency as they get larger. Small turbines are not necessarily any more efficient than diesel engines.
- tod222 13y ago> Hybrid turbine/electric propulsion has been used on trains for decades… I'd love to see a citation for this statement—it's far more accurate to say that turbine/electric propulsion has been tried for decades. Since 1969 there have only been a few test units built. [1] The largest fleet of gas turbine-electric locomotives was operated by the Union Pacific until 1969. "Fuel economy was poor" and the units were not considered a success. [2] These units are quite well-known in railroad circles. If gas turbines were as good as you say they'd be in heavy use on railroads today. Instead the dominant motive power is electric for lines already under catenary and diesel/electric everywhere else. [1] http://en.wikipedia.org/wiki/Gas_turbine-electric_locomotive http://en.wikipedia.org/wiki/Gas_turbine-electric_locomotive [2] http://en.wikipedia.org/wiki/Union_Pacific_GTELs http://en.wikipedia.org/wiki/Union_Pacific_GTELs
- zackmorris 13y agoYa true, I guess you are right. I thought trains used turbines because it would just make sense (there's no transmission, so the engines can run at one optimal speed). I'm thinking that maintenance costs/reliability issues make turbines impractical in most cases except aviation and power plants. On that note, I've never been much of a fan of turbines anyway, because they are outrageously complex/expensive. I think a Tesla turbine would be fantastic for applications like this though. For one thing, the disks could be cast out of ceramic. There must be some reason why they aren't being used (especially in hybrid electric systems like this) but I can't think of one.