Aero mod on a S-10 pick up with canopy

[omgwtfbyobbq]

Any idea on drive train losses? The car seems to have a pretty flat torque curve, so power at 4400rpm would be proportional to power at 2200rpm, hopefully. Acceleration is a bit of a PITA, because even though the car may be making whatever power constantly from ~(1-3.3k)(<- depending on gear) to 4.4k rpm, the power needed to overcome rolling/aero increases according to the square and cube of speed, so iirc we need to integrate for the first gear range, add the time to shift between gears, integrate for the second gear range, etc... To complicate matters, according to the eng-tips forum, drive train losses are minimized near half load iirc, and would follow another curve. Top speed is easy because it's one value , acceleration is a piecewise sum of ranges.

Here's a nice writeup thanks to google.

[omgwtfbyobbq]

The thing with pickups, especially small ones, is that they tend to have lots of reference area (~30ft^2), drag (~.45), but not so much weight, so if an EV driver wants to extend high speed range in a pickup conversion, dropping the Cd to ~.35 can really help. Especially considering that the minimum speed for highways is usually around 55mph...
Lets take the normal pickup, and the aeromodded pickup. Crr for both is .015, weight is 2500lbs=~11000N, at sea level ro=1.29, CdA=.98-1.26, V=55mph=~24.6m/s.
We have 11000*.015N+.5(1.29)(24.6^2)(<range>.98-1.26</range>)N=<range>547-656N</range>, so dropping the drag coefficient from .45 to .35, we increase the range by ~17&#37; at 55mph. At higher speeds, this is a greater drop since drag dominates energy consumption. For instance, dropping the Cd from .45 to .25 should result in a 40% increase in range at 75mph in the vehicle mentioned above.

[The Toecutter]

If you must know, the 40&#37; was an educated guess. But if you want to see the math that supports this, look below.


I'm going to model two hypothetical converted Chevrolet S10 electric vehicles. The truck used is a late 90s model Chevrolet S10 with extended cab.

I will assume they are using an ADC 9" motor(~85% efficient), Zilla 1k controller(98% efficient), and a single string 156V pack of Trojan T105 flooded lead acid batteries.

Lead Acid batteries have a capacity that varies with the amount of amps drawn from them. The higher the amp draw, the less capacity they will deliver. Likewise, the lower the amp draw, the more capacity will be delivered. This is known as Peukert's effect. So if you lower the amount of power required at speed, thereby lowering the amount of amps needed for a given voltage, you increase the capacity that the lead acid battery will be able to deliver. Therefore, making a lead acid battery powered electric vehicle more efficient has a double-whammy effect on range. You see an increase in range not only from the lower power draw, but also from the increased battery capacity that comes with the lower power draw.

I guessed 40% increase specifically because Phil's truck had ~30% increase in fuel economy from aeromods off of a gasoline engine. But if this estimated 40% number doesn't seem believable to you, so I'm going to back the theory up with some math and see where it leads.

At the 20 hour rate, the Trojan T105s have 225 AH of capacity, rated at 6V nominal. They have 115 minutes of reserve capacity at 75 amps, meaning they deliver a 75 amp draw for 115 minutes before running out. We can solve for the two Peukert's numbers with these figures.

Peukert's Exponent = (LOG10(20) - LOG10(Reserve Capacity / 60)) / (LOG10(75) - LOG10(20 hour rate / 20))

Peukert's Capacity = (20 hour rate / 20)^(Peukert's Exponent) * 20

From this, we get 1.236 for Peukert's Exponent and 399 for Peukert's Capacity.

The Trojan T105s have .004 ohms internal impedance as well. So as current draw increases, battery pack voltage decreases.


Below is a chart arranged in columns modelling the setups of the two trucks.

Parameter: Unmodded Truck/ Aeromodded Truck

Mass(W): 2150 kilograms/ 2150 kilograms

Drag Coefficient(Cd): .45/ .30

Frontal Area(A): 2.13 square meters/ 2.13 square meters

Rolling Resistance Coefficient(Cr): .012/ .012

Transmission Efficiency(TE): .75/ .75 (Includes stray losses like wheel bearing friction, accessories, ect.)

Motor Efficiency(ME): .85/ .85

Controller Efficiency(CE): .98/ .98

Note that the only thing that is different between the two is the aerodynamic drag coefficient.


Below is an explanation of how the above figures are used and a list of constants used:

Air Density(Rho): 1.25 kg/m^3

Gravitational Constant(G): 9.8 N/kg

Velocity(V): expressed in meters per second

Force Drag(FD): expressed in newtons

Force Rolling(FR): expressed in newtons

Force Sliding(FS): 100 newtons

Wheel Power(WP): expressed in watts

Motor Power(MP): expressed in watts

Controller Power(CP): expressed in watts

Battery Power(P): expressed in watts

Number of Batteries in String(N): a scalar without units, in the case for both trucks it is 26 since each have a single string of 26 batteries

Impedance of each Battery(O): expressed in ohms, in this case using Torjan T105s, .004 ohms per battery

Total Impedance of Battery String(R): expressed in ohms

Nominal Battery Pack Potential(VN): expressed in volts, 156V nominal in both cases since each truck is using 26 6V golf cart batteries in a series string

Battery Current Draw(I): expressed in amperes

Peukert's Capacity(K): a quantity used to determine available capacity with a given average current draw in a lead acid battery, in this case 399

Peukert's Exponent(X): an exponent used to determine available capacity with a given average current draw in a lead acid battery, in this case 1.236

Distance per Charge(D): range expressed in kilometers

Below are the equations used to simulate the two trucks:

FD = .5 * Rho * Cd * A * V^2

FR = Cr * W * G

WP = (FD + FR + FS) * V

MP = WP / TE

CP = MP / ME

P = CP / CE

R = N * O

I = (VN - (VN^2 - 4 * R * P)^.5) / (2 * R)

D = K / (I^X) * V * 3600 seconds per hour / 1000 meters per kilometer

Results for the two trucks are below:

At a speed of 26.8 m/s(60 mph):

FD = 430/ 287

FR = 253/ 253

FS = 100/ 100

WP = 20984/ 17152

MP = 27979/ 22869

CP = 32916/ 26904

P = 33588/ 27453

R = .104/ .104

I = 261/ 204

D = 39.7/ 53.8




As you can see, the range of the un aero-modded truck is 39.7 kilometers at a steady 26.8 m/s(60 mph). The aeromodded truck has a range of 53.8 kilometers at that same speed.

This is a projected increase in range of 35.5% at 60 mph, just from extensive aeromods alone.


Albeit, this is a very inefficient conversion platform that has a lot of weight using fairly high rolling resistance tires, with a huge amount of stray losses assumed(eg. chassis in bad shape adding to parasitic losses and such).

What happens if not only you do fairly extensive aeromods, but install low rolling resistance tires(eg. there are Nokian NRT2s made for trucks with a .0085 Cr), do a weight reduction by stripping away unessessary items from the interior, installing lighter seats and such(take off about 100 kg), and clean up the alignment and use synthetic transmission oil(increasing driveline efficiency to say 80% and reducing sliding friction to 50N).

Now lets compare.

Parameter: Unmodded Truck/ Aeromodded Truck

Mass(W): 2150 kilograms/ 2050 kilograms

Drag Coefficient(Cd): .45/ .30

Frontal Area(A): 2.13 square meters/ 2.13 square meters

Rolling Resistance Coefficient(Cr): .012/ .0085

Transmission Efficiency(TE): .75/ .80 (Includes stray losses like wheel bearing friction, running accessories, ect.)

Motor Efficiency(ME): .85/ .85

Controller Efficiency(CE): .98/ .98

Results for the two trucks are below:

At a speed of 26.8 m/s(60 mph):

FD = 430/ 287

FR = 253/ 171

FS = 100/ 50

WP = 20984/ 13614

MP = 27979/ 17018

CP = 32916/ 20021

P = 33588/ 20430

R = .104/ .104

I = 261/ 145

D = 39.7/ 82.0


Guess what? with all of those efficiency modifications, you've doubled the range per charge on the same battery pack! The vehicle was sufficiently heavy that LRR tires had about as much impact as the aero mods at that speed specified.

You may be asking how the heavily modified truck could be drawing about 55% of the current of the unmodified truck, but require 61% power from the batteries as that truck. Simple. Higher the current draw, greater the voltage sag. With Peukert's effect, you doubly gain on range as your power requirements to maintain a speed are lowered.



As for speed, acceleration, and other parameters, I will get to that later. I've been having a shroom flashback as I type this caused by a joint I just smoked, and I don't feel like calculating specific motor parameters(BEMF vs voltage and RPM, motor efficiency map, ect.), or crunching through a bunch of nasty integrals.

Suffice to say, I've modelled many electric vehicle concepts as theoretical examples and modelled individual people's conversions which are real world examples, and these models of real world examples have been accurate to within about 10% of what the owners of these vehicles claim they will do.

In theory, I know of a way to make a flooded lead acid battery conversion of a pickup truck that can go 200 miles per charge at 60 mph, 0-60 mph in ~18 seconds, and top 110 mph. Read the following topic:

http://www.peakoil.com/fortopic24578.html

In reality, two individuals, Brian Methany and Dick Finley, have built two pickup truck conversions with about 120 miles range at 60 mph using golf cart batteries, and they didn't have the big impact efficiency modifications such as aerodynamics.

[The Toecutter]

As for modelling Phil Knox's truck for efficiency, acceleration, and speed, we need to have the following on hand at minimum:

-Vehicle Weight
-Tire Size
-Tire Rolling Resistance
-Frontal Area(or we can estimate it by using height * width * .8)
-Drag Coefficient
-Gear Ratios
-Brake/Steering Drag Coefficient(can be estimated)
-Efficiency map of engine showing fuel consumption, BMEP, and rpm
-Power Curve of engine showing torque versus RPM at full throttle
-Efficiency curve for transmission/differential(doesn't vary much over operating range so you can get an accurate result assuming a constant)
-Weather Conditions(wind speed, air pressure, ect. It is possible to make a reasonable estimate on how much wind speed will effect drag without going into a bunch of complex AE shit)


I basically have everything on hand but the engine curves and the curves for the transmission. The engine curves are pretty much necessary to accurately model it. The transmission/differential curves aren't. Anyone happen to have curves for the engine of that Toyota T100 on hand?

I'd be more than happy to crunch the numbers and show how going from a .44 Cd to .25 Cd would affect fuel economy at 70 mph, how top speed would be affected, how acceleration would be affected. If I had to make an educated guess right now I'd say 30&#37; would be a good number for fuel efficiency, right in line with Phil Knox's claim.

[The Toecutter]

I'm curious about all these fantastic performance claims Toecutter likes to go on about, as if the entire engineering community is unaware of them. So putting a canopy and skirts on a pickup will extend range from say 100 miles to 140? If it's that simple I can't understand why he hasn't put skirts on that Sidekick or whatever it was and begin to reap the benefits of doubled FE and quadrupled top speed right away??? Come on man, start a gaslog here, throw them skirts on, and DO IT.

I very badly want to modify the Sidekick, but it is my step mom's vehicle and she said no. Otherwise I would have done so last year.

I most badly want to see how aeromods would affect top speed. Before the tune-up, it was an absolute dog topping out at like 71. While the speedo only goes up to 90 and with a recent tune-up it can now actually hit 90(drag limited), I'd be able to see how much faster it was going by eyeing the RPM gauge. With the vehicle's tires and gear ratios, in 5th gear, each 1000 rpm is 20 mph. At 90 mph, it is exactly at 4,500 rpm, 60 mph exactly 3,000 rpm. It governs out at like 6,000 rpm, but will never reach it in 6th gear from the drag. It would not surprise me if rear wheel skirts, bellypan, grill block, rear diffuser, removed roof racks, front and rear wheel spoilers, side skirts, wheel covers, removed passenger mirror, and partial boattail improved top speed to about 100-105 mph and has a positive effect on highway mpg by 15-20&#37;. But sadly, I just won't get the chance to test such mods, unless say, my step mom were to give me that piece of crap and tell me to do whatever I want with it. She has been considering a new car, but I think it is stupid since the vehicle she has is still usable. But there isn't much convincing her...

I do have two cars under my name, both of which aren't yet road legal. I have the 1996 Ford Contour that needs engine repairs and needs to have its emissions system replaced to pass inspection(I used to drive it as a teenager until it developed engine problems and was taken in to get inspected and it didn't pass emissions), and I have the 1969 Triumph GT6 MkII that is undergoing a restoration and conversion to an electric vehicle. Once I get the Triumph going, I certainly will experiment with that and certainly will report the results here. As for the Ford, it would probably be cheaper to convert the Triumph to a simple 60-70 mph capable electric car with contactor controller, bridge rectifier charger, Prestolite motor, and 144V pack of Universal Battery UB121100 AGMs. That's doable for about $2,000 more. Therefore, the Triumph is what is getting my money.

I would keep a gas log of the Sidekick if I had an accurate way to keep track of the fuel used and miles driven. The problem is that it is not an OBD-II(therefore not scan gauge compatible), and even if it was, that $250 for a scan gauge would be better spent on the Triumph. Further, my dad and step mom both use the vehicle too, and sometimes they put gas in it just as I do. I'd have to pester them for the numbers each time they put gas in it, and if they don't have them, it ruins any validity for the experiments. The only time I've been able to get any reasonable fuel economy estimates is when I've started a set of trips with a full tank and refilled it myself, and I imagine the error is about 10% or so given that all I have to rely on is the fuel gauge needle, the odometer, a gas pump, and the fact that it's a 12 gallon tank.

I'm curious about the equations you use to arrive at this data. Run these numbers and tell me how fast this thing accelerates and tops out at:

2800 lbs
100 hp
22 sq ft frontal area
Cd .37

Let me guess? Your Tempo?

I won't be able to calculate top speed unless I have a map of the engine.

Acceleration needs an engine torque vs rpm map at full throttle to be calculated accurately. But it can be reasonably estimated +/- 10% with power to weight ratio.

(Mass in kg)/(.9 * horsepower) = 0-60 mph acceleration time in seconds is a commonly cited rule of thumb for a gasoline powered car.

So, using this estimation, 0-60 mph of this 100 hp, 2,800 pound car is 14.1 seconds. My friend timed his Ford Tempo GL from 0-60 mph and got like 15 seconds. He has the 98 HP 2.3L HSC L4 engine.



I can fairly accurately estimate fuel consumption though, but it may be a little off without a specific map of the engine and instead using the graph below to estimate how the engine will behave in regard to efficiency:



Mass(W): 1,270 kilograms
Drag Coefficient(Cd): .37
Frontal Area(A): 2.05 m^2
Rolling Resistance Coefficient(Cr): .010
Transmission Efficiency(TE): .8 (Includes stray losses like wheel bearing friction, accessory loads, ect.)

Velocity(V): expressed in meters per second, in this case 30 mph or 13.4 m/s
Force Drag(FD): expressed in newtons
Force Rolling(FR): expressed in newtons
Force Sliding(FS): 30 newtons
Wheel Power(WP): expressed in watts
Motor Power(MP): expressed in watts
Engine Efficiency(EE): thermal efficiency of engine at given load expressed as decimal
Fuel Power Required(P): expressed in watts, the rate at which gasoline is being used(33,800 Watt hours in a gallon of gasoline)

Air Density(Rho): 1.25 kg/m^3
Gravitational Constant(G): 9.8 N/kg

Equations used:

FD = .5 * Rho * Cd * A * V^2
FR = Cr * W * G

WP = (FD + FR + FS) * V
MP = WP / TE
P = MP / EE

Results:

At 26.8 m/s(60 mph):

FD = 340.5
FR = 124.5
FS = 30
WP = 13266
MP = 16583

The motor itself is 67 kW peak power. You are using at 60 mph 16.583 kW of motor power to maintain speed. This is 25% engine load. Looking at the graph above, you get roughly 24.5% engine thermal efficiency.

So:

P = 67686

At 60 mph, you are using 67.686 kW worth of fuel while the engine is outputting 16.583 kW.

(33800 Wh / gallon) / (67686 W) * (60 miles / hour ) = 29.96 mpg


Your Tempo would thus get an estimated 30 mpg at a steady 60 mph from the above. How accurate is this? The EPA rates it at 28 mpg highway, for comparison.


The above graph is very flawed, because it doesn't factor in RPM, and a real BMEP vs RPM map has circular shapes representing a certain amount of kWh per gram of fuel delivered for given areas on the RPM versus BMEP graph. It's often graphed in two dimensions sort of like an elevation map.


Using the above methodology, if you were to cut your drag coefficeint to .20, you'd need 11,341 kW produced by the motor at 60 mph, giving you 17% engine load, giving you 22.7% thermal engine efficiency, and you'd get an estimated 40.6 mpg.

This would be an estimated 35% improvement in FE if you got your drag coefficient down to .20 and no other changes whatsoever.

LRR tires(Cr .006), synthetic tranny oil and zeroed alignment(now .85 efficiency for transmission, 20N sliding friction), reducing weight by 150 kg, along with lowering drag coefficient to .20 would get you an estimated 50 mpg at 60 mph.

All of these cases are with no engine modifications at all.

Sadly, I do neglect cross winds and other factors like such, and again, that graph is general and doesn't account for engine RPM.

Find me a specific map of your engine, for both torque vs rpm, and BMEP vs RPM vs kWh/g fuel efficiency, and I will do my best to model how all of this will affect the performance of your ride.


***note***

I typed 67 kW when the engine actually is 73 kW. Misconversion from HP to kW on my part. Oh well. Shouldn't affect the results much, as the only thing this number was used for was finding percentage engine load. Probably remove about 0.5 mpg from it or so.

[omgwtfbyobbq]

Originally Posted by The Toecutter

I won't be able to calculate top speed unless I have a map of the engine.

Sure you can! Peak torque is ~124ft/lbs@2200rpm, and at peak power it's making ~115ft/lbs, so imo it's a safe bet that the power curve of an NA gas engine between those two points in the rpm range is fairly linear. As long as power doesn't drop to crap between 2200rpm and 4400rpm, peak power is peak power is peak power, and the car is either limited by drag, or gearing... Probably drag in this case.

[The Toecutter]

I'll go by your assumption then. It seems about as reasonable as the other estimates I made, but my knowledge of the internal combustion engine is limited.

I am going to assume part of the engine curve looks like the following based on what omgwtfbyobbq says:

2200 rpm, 39.3 kW
2500 rpm, 44.0 kW
3000 rpm, 51.7 kW
3500 rpm, 59.5 kW
4000 rpm, 67.3 kW
4400 rpm, 73.5 kW

If linear, from 2200 rpm to 4400 rpm the horsepower output can be approxamated by the equation:

kW = (rpm - 2200)*(.015545) + 39.3

This will allow us to figure out how much horsepower is being made when the car is being either drag limited or governed.

Below the following parameters will be used as you specified:

Mass: 1,270 kg
Drag Coefficient: .37
Frontal Area: 2.05 m^2
Rolling Resistance Coefficient: .010
1st * Final Drive = 11.973
2nd * Final Drive = 7.908
3rd * Final Drive = 5.185
4th * Final Drive = 3.805
Overdrive * Final Drive = 2.872
Drive efficiency(including stray losses) = .8
Tire Diameter = .61214 m

v = speed in m/s

v = Tire Diameter / (gear ratio * 19.091 / rpm)

Now we can lay out a road speed versus RPM versus power required versus to maintain speed versus power at full throttle chart in the overdrive gear.

Road Speed - RPM - Power at Full Throttle - Power to Maintain Speed

26.8 m/s(60 mph) - 2400 rpm - 42.4 kW - 16.6 kW
40.2 m/s(90 mph) - 3601 rpm - 61.1 kW - 46.2 kW
44.7 m/s(100 mph) - 4004 rpm - 67.3 kW - 61.5 kW
45.1 m/s(101 mph) - 4040 rpm - 67.9 kW - 63 kW
45.6 m/s(102 mph) - 4084 rpm - 68.6 kW - 65 kW
46 m/s(103 mph) - 4120 rpm - 69.1 kW - 66.6 kW
46.5 m/s(104 mph) - 4160 rpm - 69.8 kW - 68.6 kW
46.9 m/s(105 mph) - 4201 rpm - 70.4 kW - 70.2 kW
47.3 m/s(106 mph) - 4237 rpm - 71.0 kW - 71.8 kW
47.8 m/s(107 mph) - 4281 rpm - 71.6 kW - 74 kW
48.2 m/s(108 mph) - 4317 rpm - 72.2 kW - 75.7 kW
48.7 m/s(109 mph) - 4362 rpm - 72.9 kW - 77.9 kW
49.1 m/s(110 mph) - 4397 rpm - 73.5 kW - 79.6 kW

You can see in the above chart that the Tempo will top out at 105 mph in stock form. In real life, I recall that the 98 hp version does like 107 mph(even have another source claiming that(here)), even though the speedo only goes to 80. This is very close. The 86 hp version does exactly 100 mph according to a variety of sources, and this is off by about 2 mph as well in that chart. I was going to solve it using calculus and algebra, but I figured it would be better to make a chart to illustrate how the car is behaving at various speeds.

Looks like the figures I used for my fuel economy calculations were pretty dead on in regard to the forces that the car would be subjected to, if the top speed calculations are this accurate(pessimistic by 2 mph). If I could get a specific fuel consumption map of the engine, I could have some very accurate FE numbers.

What would happen if you got the drag coefficient to say a modest .34? your top speed would increase to at minimum 110 mph. This should be achievable with a simple belly pan by its lonesome, if done correctly. If you got Cd to .20, top speed would be much, much higher(maybe even reach the rev limit of 5200 rpm, which would correspond to 130 mph!), but I have no way of approxamating the engine curve past 4400 rpm, unless someone could give a reasonable estimation or provide the curve itself.


If these numbers are accurate, modding the fuck out of your Tempo should get around 50 mpg highway, including not just aeromods, but LRR tires, small weight reduction, synthetic tranny oil, ect. Taller gear ratios and larger tires could boost that even more, probably around 5-10% judging by the success of taller gear ratios on this site.

Done right, I think your Tempo could see ~55 mpg highway, and potentially 130 mph top speed.



I've run these calculations for the Sidekick, assuming I can get Cd down from a high .48 to about .35, and I'd get ~32 mpg at 60 mph and 105-110 mph top speed may be possible. Do more than just aeromods, it could potentially get 35-37 mpg highway at 60 mph. But it isn't mine to experiment with.

[The Toecutter]

I wonder where this dude went? I'm dying to know more about that truck!