Part 1: Overview:
All objects .....cars, motorcycles, bicycles .....and you! .....when moving through air .....create friction and drag. On earth, the pressure of the atmosphere causes a higher pressure at sea level, than it does on a mountain top. The higher you go with your motorcycle, the faster you should be able to go, theoretically, due to less friction with the air ....OR; conversely, the less power from your engine you would need at the same speed as at sea level; due to the reduced air drag. While friction and drag are not the same, you can regard them as the same for this particular bit of reasoning, which, other things not considered, is true about the speed, etc.
As altitude increases the oxygen content of the air is less (by weight), and your engine will have less power as you go up in altitude, which can totally offset performance increases from less air drag/friction. Usually performance suffers as altitude increases, particularly above 5000 feet. In some instances, fuel mileage WILL increase with an altitude increase, especially on fuel mixture compensating engines, such as those with fuel-injection. On some uncompensated carbureted vehicles, mileage may decrease substantially. Sometimes supercharging or turbocharging can improve fuel mileage, particularly with small engines with smaller combustion areas (cylinders and heads). MANY small factors also enter into fuel mileage.
CARS, especially modern ones, are generally designed to slip through the air with relatively low friction and drag, so as to get the best possible fuel mileage consistent with such as body shape appeal and other factors. Manufacturers generally do everything reasonably possible to reduce friction and drag within design and function restraints, due to various government-imposed penalties for poor gas mileage, not to mention selling features. Of course, there are limits to designs that would be acceptable or practical. The shape of the car, friction of tires, closeness to the ground, irregularities in bodywork and under the car, and literally many hundreds of things, all have plus and minus effects on fuel mileage.
Motorcycles are generally designed for performance, not necessarily fuel mileage; although that is or can be a factor. There are large differences between various motorcycles depending on what the designers/engineers intended. Some motorcycles are designed for strictly for performance; particularly regarding acceleration, top speed, and stability at high speeds. Some may well be quite compact, presenting a small surface area to the oncoming air, which helps fuel mileage.
When an engine is designed for performance, fuel mileage will almost always suffer. Motorcycles into the late eighties used carburetors having rich mixtures (especially before ~1980), for better power and performance. Even with fuel injection, mixtures on SOME high performance bike engines tend to be 'somewhat' on the richer side; using more fuel. This is particularly so for high performance motorcycles. In particular and quite notable, camshaft timing and other such 'tuning' is such that fuel tends to be wasted during aggressive acceleration.
In all engines, fuel is used for COOLING the burning mixture, and a slightly more fuel-rich mixture will usually provide more horsepower. This wasting of fuel is much more pervasive during fast acceleration, than at constant road speeds.
As speeds rise, the power required greatly increases. Fuel usage is not on a flat upwards curve with speed ....rather, it is a very steep curve. This is particularly so on vehicles with high coefficients of drag. I will get into this in depth later in this article. The basic idea you should have at this point of discussion is to consider not acceleration, but constant speed ....and the idea here is that for every same increment of speed increase, the fuel required becomes more than for the previous increment. If you were traveling at a constant 50 mph, and previously had been at a constant 45 mph, you used a certain amount more fuel per mile, for the extra 5 mph of speed. For 55 mph, you use MORE than the just the extra amount for the 45 increase to 50. FURTHER, the faster you go, this idea continues, and is on a fast rising curve. It actually approaches a cube function! F³
In the classical way of thinking about friction and drag, one converts by one means or another the ongoing face and structure of the vehicle into a equivalent 'flat plate', of some number of square feet and square inches, and then calculates using commonly known mathematical formulas, the Coefficient of Drag, Cd.
You could do that yourself, by taking a photograph from the front, enlarging it greatly, and then calculating the area of things and of no things, in the photograph. If the photograph was full size, you could, with some effort, calculate the number of square feet and square inches, of effective frontal area. The answer would not REALLY be completely accurate, however, as all those air flows around and in-between everything DO interfere with each other, making things WORSE than calculations by area alone. But, you would get some decent information about Cd ....at least as far as converting to flat plate area. In the real world of doing this, you could make a huge chart with small identical-sized squares, and then doing area calculations. For over-all design purposes, Cd work is almost always done by means of a wind-tunnel with full instrumentation; and preliminary work is almost always done by means of 2D and 3D computer software. Special software programs are used with computers to do the final analysis of the wind tunnel measurements.
Road-going production motorcycles generally have lousy CD, compared to any modern car. Thus, a motorcycle uses a fair amount of horsepower to maintain any speed, let alone accelerate or get to high speeds. Using horsepower means using fuel. Increasing engine efficiency in its burning of fuel has a VERY SMALL effect, compared to Cd. A large bike getting perhaps 38 to 44 mpg in steady riding at perhaps 60-75 mph, might gain as much as 5 mpg more by going from carburetion to fuel injection, with a few other changes ....and maybe a few more mpg if the rear drive ratio was flatter (allowing the engine to turn more slowly).
All road-going vehicles have TIRE friction with the road that produces heat. That friction is needed, but it is a user of horsepower. It could be thought of as power that the engine produces that ends up as heat from the tire friction (from contact, squirming, shape change, etc.) that is transmitted into the road surface ....and into heating the tire itself. There are other ways of thinking about this sort of thing ....such as the air resistance of the tire/wheel combination to-the-surface, effects of the wheel spokes, and many many other small things ....all of which tend to add up. These effects also use horsepower in maintaining any given speed.
So, what is typical fuel mileage for an Airhead, in fact, what's typical for most motorcycles?
Depends MOSTLY on how you ride ....aggressively; higher speeds; higher rpm; on and off the throttle; ...etc. Alcohol in fuel lowers fuel mileage, by 4% to 8%. High ratio rear drive lowers fuel mileage; typically this is another 5%. Saddlebags and tail trunk lower mileage. Many windscreens lower mileage. Sitting very tall in the saddle lowers mileage. Passengers usually cause a lowering. Richer settings in the carburetors beyond the optimum setting will always lower mileage. Side winds and head winds will reduce mileage, sometimes drastically. Probably 35-48 miles per American-sized gallon is typical for most Airheads, at varying but legal speeds. A few motorcycles, any brand, will get as much as mid-fifties, and if driven quite moderately, as much as 60; others will be in the high twenties. Airheads can sometimes reach 50 mpg+-. Your average speed is quite important. As speed increases, mileage goes down on a steepening curve.
The chart just below can be plenty informative. Note the last item, the common brick, in the first section.
0.0224 F4 Phantom fighter jet
0.189 VW hybrid diesel-electric model VW XL1. Requires only 8.3 Hp to maintain 62 mph
0.25 Toyoto Prius, all models/versions are approximately this value
0.26 BMW i8 hybrid car; Mazda 6
0.28 Snowbum's Alfa Romeo Giulietta Sprint Specialé; C6 Corvette.
0.303 Honda, 1996, RS125GP
0.32 2015 Mazda Miata
0.33 Subaru 2014 Forester
0.35 Lexus LX570 SUV. An amazingly good Cd for such a big vehicle.
0.38 BMW K1, rider sitting upright.
0.43 BMW K100RS, rider sitting upright.
0.495 BMW K100RT, rider sitting upright.
0.562 Vincent Black Shadow, rider sitting upright.
0.6 Approximate for the Suzuki Hayabusa, a very well-designed & slippery street bike.
2.1 Common brick used in construction (no, don't know the orientation, think it was sideways)
Vehicle Drag Coefficient
Description Low Medium High
Experimental 0.17 0.21 0.23
Sports 0.27 0.31 0.38
Performance 0.32 0.34 0.38
60's Muscle cars 0.38 0.44 0.50
Sedan, newer 0.34 0.39 0.50
Motorcycle 0.50 0.90 1.00
Truck 0.60 0.90 1.00
Tractor-Trailer 0.60 0.77 1.20
The following information was derived from wind-tunnel measurements, and is expressed in different units. The conclusions you will make are quite valid!
Cd (as drag area) VEHICLE
5.54 Ferrari 308 GTB, year 1980
5.61 Mazda RX-7, year 1993
5.92 Porsche 911, year 1994
6.24 Toyota Prius, year 2004
6.27 Porsche Carrera, year 1986
6.81 Subaru Legacy, year 1989
7.34 Honda Civic, 2001
7.57 Toyota Camry, year 1992
8.71 Buick LeSabre, year 1991
16.8 Hummer H3
18.06 Hummer H1, year 1993
26.3 Hummer H2, year 2006
Want to know about other vehicles?
Want to know Cd, and not CD-A, what about total drag?...try the links below.
NOTE: Cars generally have the edge over bikes, as speed increases greatly, due to the dynamic characteristics.
Part 3: Getting into the actual mathematics:
I put two formulas below, and will do a bit of discussion about each. These are not my made-up formulas, but well-known classic formulas.
Fd = (1/2) Pv2 ACdV
It is at this point that confusion sometimes comes about, and arguments can start.
That is because fuel usage...and horsepower requirements...are NOT proportional to the square of the speed. The confusion and arguments probably come from MISUSE of the information in TWO formulas. You can NOT use just ONE of these formulas & gain an understanding. They MUST be combined or both used with understanding. Because of the complexity I have NOT combined the formulas, because I want YOU to easily understand the reasoning why the increased horsepower required for a higher speed is not proportional to speed, nor to the square of the speed....but is proportional to an even higher figure.
Power required = Av + Bv2 + Cv3
Let's take a look at that formula:
A is the resistance....which includes the tire rolling resistance...this is a linear function.
B is mostly concerned with internal engine friction components.
C is the aero-forces, including the coefficient of drag, air density, and so on. NOTE that, as opposed to the previous formula, C is being multiplied by v cubed and added.
v, as before, is the velocity, or speed
As earlier here, there is no need for you to get deeply into the formula. The important part is actually simple. The power required is proportional to the CUBE of the VELOCITY (speed, that is) as far as as the external things are concerned. NOTE that POWER is directly proportional to fuel consumed.
How to reason it all out, if you are still confused by the math:
Part 4: Additional information:
There is a LOT of VERY wrong information on the Internet, and even in printed books, about Cd, Cd-A, etc. MUCH of the wrong information is due to those persons who are writing these things failing to understand that TWO formulas are in play, and must be used TOGETHER. Many do not understand CD, nor the effect on Cd from various object shapes. Many of these websites are done with lots of mathematics, and look scholarly. I think many copy from each other, re-arrange things, and think they know what the truth is. In my discussion of Cd, and Cd-A, above, I have simplified things for your easier understanding. Here is a link to something written by Tony Foale on aerodynamics. Tony's work you can generally rely on.
I am aware that few of you will take the time to really read, think, etc., about the minimal math in this article ....but I HOPE some of you DO, andI hope ALL of you take away the real reasons for lousy motorcycle fuel mileage, and the principles, at least in a broad sense, of why fuel mileage goes down so very fast as speed rises ....and why this happens so quickly with motorcycles.
Part 5: Equivalents/conversions:
cubic inches x 16.39 = cc
liters x 61.02 = cubic inches
cubic inches ÷ 231 = gallons
Imperial gallon x 1.2 = U.S. gallon
mpg x 0.354 = km/L
km/L x 2.825 = mpg
Km x .621 = miles
one Km is approximately 5/8th of a mile.
Part 6: Pumping losses, engine friction, efficiency versus load, cruising RPM considerations:In the mathematics in this article (up to this point) not every possible item and effect is discussed. The inefficiency, that is, less-perfect, use of carburetion versus fuel injection is barely dealt with. Engine pumping losses are not discussed, which can be high, and should be considered, especially for carburetor bikes. Pumping losses are relatively high in any engine, no matter if carbureted or not; particularly at part-throttle.
A gasoline 4 stroke engine is more fuel efficient at higher loads. Engine friction from JUST RPM is often said to vary linearly with RPM, which is close to the truth. FRICTION uses up horsepower.
A primary reason that the engine becomes less efficient as you close the throttle is due to pumping losses. MOST gasoline 4 stroke engines have a throttle plate butterfly valve, perhaps called by that name. Motorcycles with fuel injection to a manifold, and also slide-only carburetors can both be lumped in with those. There are several types and situations of pumping losses, but, I am using the term to include them all. Pumping losses are a MAJOR effect.
One thing often not thought-of, is that, at its core basics, our engines are HEAT engines. That is, the combustion process produces heat, and expanding gases. The force of the expanding gases (rise in pressure) moves the pistons inwards, which produce the power we lust after. The energy in the combustion process is very IN-efficient, and a LOT of the energy is sent out the exhaust system, and a fair amount is also radiated into the air, for cooling. It takes a lot of power to just make the engine move AND TO COMPRESS THE FUEL-AIR, BEFORE IT IS IGNITED. Pumping losses!
The chart below is self-explanatory. One can expect somewhat of a similar chart for any given engine. Do not idly take a quick look and pass this chart by. STUDY THIS CHART!!
ONE thing even a brief look at this chart will tell you, is that the gearing ratios from crankshaft to rear wheel is important. For the Airheads, assuming 4th gear (4 speed transmissions) or 5th gear (5 speed transmissions), where the transmission ratio is identical (1.5:1), the rear drive ratio has a noticeable effect on fuel mileage, both for over-all real world driving, AND constant speed driving. Read the next sentence carefully:
It is obvious from the chart that using a fair amount of throttle at lower rpm, roughly 3,000 here, gives the best mileage.
For the engine for which this chart applies, you can see that around 4000 rpm is a good rpm for typical cruising on the open road, but if at much lower speeds, cruising at 3300 rpm will give good fuel mileage. NOTE that the chart below is not that of an Airhead engine, but the idea, and curves shapes, are typical. In real terms, if you increase the rpm listings of rpm at the bottom of the chart, from 1000-5000 rpm as shown, to be re-marked to 2300 to 5800 or so, that is REAL ....at least from what I remember when having MY R75/5 on Axtell's dynamometer (I also did extensive work on the dyno with my Nor-Vin).
As you can see, the fuel consumption varies with both load and rpm. You could consider this to mean that at a constant speed, on a flat or constant rising road, there is an optimum throttle amount. It is generally bad for an engine to 'cruise' at very high throttle settings and very low RPM. That is called "lugging". For the BMW Airhead engines, due to the design, including primary balancing rpm area, and many other factors, the engines will, OVERALL, prefer to be at 3800-4500 rpm, under mild or relatively flat road conditions. That is, the throttle will be at, perhaps, only about
35%-60%. There is nothing all that strict about this.
HOWEVER, as you increase the throttle (but keeping the rpm in that above 'sweet spot'), perhaps doing this by shifting to an appropriate transmission gear, mileage goes up. Don't overdo this. There are many rear end ratios used on the BMW Airheads, so I cannot give hard and fast rules, except what I said above, ~35-60% throttle, and ~3800-4500 rpm. The engines are certainly capable of cruising vast distances at much higher throttle and/or rpm, but fuel mileage suffers more.
Note: if you are in any gear, with a constant throttle setting,...... & opening the throttle some additional amount does NOT
accelerate the motorcycle, then you ARE in the LUGGING AREA, so SHIFT DOWNWARDS as needed!!! Lugging increases cylinder pressures, and heat, and, if excessive, WILL CAUSE SERIOUS ENGINE DAMAGE!
Here is another fuel-robbing situation. Did you ever think that an alternator uses engine power? If you are using even near full output of the 280 watt stock alternator, the alternator, being less than 85% efficient, will pull a considerable amount of engine power to produce this electricity. The effect on mileage is WORSE at lower speeds.
There are other things, such as rear drive ratios. The higher the numerical ratio, the more RPM for a given speed, the more friction losses in the engine, and the more throttle is used.
Things ADD UP!
PART 7: Fuels, jetting, poor mileage due to problems, ETC. There can be many reasons for poor mileage; here are SOME of them:(1) Alcohol-laced fuels (Gasohol) has already been mentioned.
Part 8: RAM AIR:Sometimes folks ask questions about RAM air possibilities for "no-cost" supercharged horsepower. Dynamic air pressure by or on a moving object are treated by engineers as a certain size of flat plate moving through the air at some speed. As you read earlier in this article, drag is proportional to the square of speed. Drag can be said to be dynamic air pressure. As we have seen earlier in this article, Dynamic air pressure is proportional to the SQUARE of speed, but the horsepower to attain that speed goes up as the CUBE of that speed change. Think about that! This means that for oncoming air, just the SPEED change, is proportional to the cube of gasoline usage.
But, the question here is the use of RAM AIR for supercharging purposes; so, I will give an example:
So, 0.33 psi is quite small compared to atmospheric pressure forcing itself into the cylinders (about 15.0 psi at sea level). Thus any ram-air-supercharging effect is very small .....until speed gets VERY high. However, once the speed is high enough, the pressure rise is more and more usable ....because of that SQUARED function I mentioned earlier. Speed starts to make some reasonably usable difference around 150 mph, all things considered. Thus, ram air pressure does NOT help at ordinary road speeds. AND, no, 'big scoops' don't increase that pressure and performance due to the mathematics and area involved.
Part 9: Horsepower, Torque, miscellaneous:1. Several methods of 'proving an increase in performance' come to mind. The best testing is on a dyno (dynamometer)....with the temperature and humidity of the incoming combustion air being measured and written down and accounted-for; and having fuel flow instrumentation. Dyno's cost $3K upwards, and are expensive to rent. But, they are really great, especially if you use the same dyno for all testing. That is because a decent dyno is good enough to compare between readings on the SAME dyno; but not all that great for absolute measurement values. Very fancy dyno's can cost over $100,000.00. 2. The second best method is often a top speed run, same loading/equipment and rider position, clothing, etc. You can compare, before & after modifications. Use the same road area, same temperatures, same atmospheric pressure, same wind (if any), same direction. Calculations could be done based on actual measured increase (or decrease) in top speed, to get an idea of the real Cd. Runs in two directions within minutes tends to average out any wind. Yes, if you are a bit clever, you can calculate Cd from performance increases from the basic Cd formulas.
Premium fuels versus mileage and combustion temperatures:
There is an old controversy over possible increases in combustion chamber temperatures, ETC., when using premium gasoline's in lower compression BMW airhead engines, where higher octane is supposedly not needed.
Gasoline burns at about the same rate under normal, that is, not detonating, etc., conditions. The output (BTU) per gallon of Premium gasoline is potentially ....or even likely ...to be a small amount LOWER than for Regular. I think it is likely that SOME premium gasoline's WILL give LOWER gas mileage than a regular gasoline will .....assuming here that the engine will run properly on Regular grade gasoline in the first place.
Temper this with the fact that gasoline formulas change, and also change between summer and winter grades of gasoline. Winter gasoline contains rather volatile things like butane or propane. In the West, California in particular, oxygenates were added to most fuels for decades. These additions GENERALLY cause ~5-10% POORER gas mileage. They are NOT good for your engine, carburetors, hoses, etc. Nowadays, ethanol is added to nearly all road fuels. Without jetting changes, they make an engine run leaner. The fuel mileage decreases from just the ethanol content ....AND! ... decreases even more, perhaps another several %, when you rejet for performance with such fuels.
05/25/2009: initial release.
01/03/2010: slight updating
09/28/2012: Add QR code; add language button; update Google Ad-sense code, add Additional Information section
10/04/2012: Merge information from hp-drag.htm article, so that one can be eliminated. Go over the whole article.
12/09/2012: Add shapes chart
03/05/2013: Add comments "Some Special Details" and the fuel-rpm-load chart
09/02/2013: Clean up article. NO important details changed. Language button removed sometime in 2013.
01/18/2014: Clarify some details.
03/05/2014: Updated in several areas, add more vehicles, charts, conclusions
12/04/2014: Expand article more regarding Cd, with more charts and comments
03/04/2016: Meta-codes; left justification; metatags, etc. Still needs narrowing and final meta's, etc....to be done later this year.
06/28/2016: Update metacodes, scripts checked, improved descriptions, enlarged font sizes, full justify left, full length lines, etc.
08/02/2016: Add section, prev. in InExTuning article: Premium fuels versus mileage and combustion temperatures.
01/23/2017: Fix totally wrong hyperlink in Part 7 (4). Also clarified some things in Part 6.
03/27/2017: Fix typos, improve clarity.
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Last check/edit: Monday, March 27, 2017