This article, and its associated speadsheets, represent the personal views of Keith Tynan (aka BRG). Whilst every effort has been made to make sure they are accurate, no liability can be accepted for any mistakes contained in or use made of these data.
I would point out that although I have a scientific background, I am not a professional in this area, and I would be grateful if this material was not referred to as definitive.
However, if something's wrong please let me know:
BRG - mailto:keith@headway-ltd.com.
This article is the result of a personal exploration into the theory of motorcycle engine and transmission design. It is oriented towards trying to fill the gap between dynamometer graphs, manufacturers' specifications and road test data, using a theoretical approach. In particular, it is geared towards understanding the relationship between engine power and torque, and the effects these have on the performance of a bike. Last, but not least, it attempts to identify the characteristics of maximum acceleration.
I've tried to use this article as a repository of information that I've gelaned from a variety of sources, and to present it in a way that is meaningful to me. So apologies in advance if things are a bit unclear, or incomplete, as I have my own set of fundametal axioms that I tend not to repeat, and current issues which I explain in a lot of detail.
This article attempts to substantiate the following postulates with regard to motorcycle engine power and torque:
a) Maximum overall acceleration is achieved at maximum power.
b) Maximum acceleration in any one gear is achieved at maximum torque
The spreadsheets contain many simplifications - the topic is a complex one!
Each of the following Excel spreadsheets contains six graphs.
(You may encounter problems if trying to follow these links using Netscape. You may try to right click on the link and choose the 'save link as' option - but this doesn't work with NS 4.5 or 4.7)
I make no aplogies for the fact that the spreadsheets are based upon SI units.
Hyperlink |
Bike |
Data source |
|---|---|---|
1968 Honda CB250SS |
[R1] & BRG recollection |
|
1994 Triumph Trophy 3 |
Das Motorrad 1991/08/17 & Bonz dyno data |
|
1997 Honda CBR600F (std + modified) |
Clay dyno data |
|
1999 Ducati 996 Biposto |
Bike Magazine January 1999 |
|
1999 Ducati ST4 |
Bike Magazine February 1999 |
|
1999 Triumph Daytona 955 |
Bike Magazine January 1999 |
|
1999 Triumph Sprint ST (std + BRG) |
Bike Magazine February 1999 & BRG dyno data |
Notes
1 My ST's data (BRG) are taken from a run on a Fuchs BEI 251 dynamometer. This is an inertia dyno, which means it only gives readings when the roller is being accelerated/decelerated. The print-out from this dyno gives values for crankshaft, gearbox, wheel and roller (i.e. road) power & torque. The roller torque is measured directly during acceleration. The total frictional loss from wheel to crank is measured during decelerating with the throttle closed. The gearbox and wheel torques are calculated by combining the measured losses with data held in its database of the motorcycle configuration. The configuration data take into account the theoretical transmission efficiency and rotating inertiae of the engine and transmission parts of the specific bike being tested. (Fuchs guarantees this accuracy to within 3% although 1% is typical.) The losses between the tyre & the roller (slippage) are measured separately and are also taken into account. The frictional losses from the rear tyre are understood to form part of the Fuchs losses (though these approximate to a constant (2% of total mass) for the subject speed range).
2 Bike Magazine's graph data for the ST (max 109 bhp) and the Ducati ST4 (max 102 bhp) and Ducati 996 BP (max 111 bhp) closely match their factory specifications of 108/103/110 bhp (crankshaft) respectively, so this is taken as an indication that the graphs show crankshaft data. The graph data for the Daytona (max 116 bhp) present something of a problem. The magazine text implies that the dyno figures are from the rear wheel, quoting maximum crank power of 123 bhp. Although 123 bhp would be closer to the factory specification (128 bhp - crankshaft), these data are assumed to be crankshaft measurements, as the ST, ST4 and 996 graph data match the factory specification (crankshaft) power, and the 996 was tested at the same time as the Daytona. Although there are inherent differences between the frictional losses of a twin (Ducati) and a three (Triumph), the same frictional losses (from my dyno run) have been applied to all bikes in the absence of empirical data.
This graph shows the power and torque obtained at the crankshaft.
The power data are taken from the data source, which may be either a magazine article or a dynamometer run. The torque data are calculated from the power data - there being a fixed relationship between power and torque.
Crankshaft power does not account for any transmission losses, though in cases where the data source quotes power figures from the rear wheel, efficiency adjustments have been made to derive the crankshaft figures. These adjustments have been taken from the author's Sprint ST dyno run on a Fuchs dynamometer, and applied to all spreadsheets (with the exception of the Honda CB250, for which findal drive losses are assumed to be smaller). This is a necessary simplification, as data for individual cases in not available.
It is not practical to talk of ideal power and torque curves. However, a simple torque line would be a flat horizontal line over the available engine speed range. This would correspond to a straight (inclined) power line. Such lines can be seen as a reference to explain the relationship between power and torque, but there are many reasons why this would not be ideal.
There seems to be a consensus that the resulting power/torque delivery should be smooth, with no rapid changes, so that acceleration is bears a fixed relationship to throttle opening.
Power and torque readings (e.g. from a dynamometer) are affected by air temperature, pressure and humidity. To facilitate comparison, the data are adjusted - or normalised - to standard pressure, temperature and (sometimes) humidity values. There are three main normalisation standards in use by the bike media:
The values of one standard cannot be directly compared with those of another, they must be adjusted. Further details are given in the 'Assumptions' section below.
Only my own Triumph Sprint ST data (BRG) are of a known standard (EC 95/1). The rest are unknown, and no conversion has been applied.
This shows the relationship between crankshaft power and road speed. It's overlayed with the measured maximum speed (white) and the rpm corresponding to maximum torque (dashed black).
Each of the power curves shows data markers at 1000 rpm intervals, with the first and final points as per the source data.
This graph illustrates the change-up points to achieve maximum acceleration:
A bike won't be able to accelerate beyond the white line (unless it's going down hill, or has a tail-wind).
This is perhaps the key graph of the whole set.
It plots the driving force against road speed, and shows:
This graph shows the following features:
Note that the max power curve (thin black line) is a virtual curve. Because the gears are fixed and at intervals (rather than continuous), it only exists at the points where it touches the gear lines (the touching is exact - any discrepancies are a result of Excel's line-smoothing algorithm).
Were the max power curve to exist, i.e.we had infinitely variable gear ratios, it can be seen that max power would provide the greatest force at any particular road speed.
It also endorses the point that the quickest get-away from a stand-still is by holding the engine at max. power, and slipping the clutch so's to maintain optimal traction (ca. 2-3% slip). This would provide something approaching an infinitely variable gearbox - up to first gear! (Note that although there would be a considerable penalty in increased frictional losses, the available power would almost always be more than enough for optimal tyre grip for larger machines.)
Consider the case where we're riding along in say fourth gear, somewhere between max torque and max power. If we encounter increased resistance, due to say a increased wind pressure when passing a lorry, this tends to make the engine reduce speed. If we are inside this userful operating range, a reduction in speed will mean that we have more force to overcome the 'obstacle'.
Consider now the case where the same thing happens, but we are below the torque peak. the increase in resistance forces us to lose speed, and we have less power to overcome the obstacle.
Although in the normal course of events, such obstacles are unlikely to cause difficulty, this operating range is a useful (empirical) guide to the flexibility or ridability of the bike.
One index of elasticity (there are many!) is given in the blue fields at the top of each spreadsheet.
Finally, the TE Cadence graph also shows the effect of gradient the the selected gear and maximum speed. (It can be adjusted by a green cell on the right-hand side of the sheet.)
The TE cadence chart also shows the effects of relative air resistance of each machine, The measured top speed has been used to define an air resistance index for comparison purposes. This is the cell marked 'Drag coefficient' on the left-hand side of each sheet. Air resistance is actually a function of cross sectional area, drag coefficient, air density and bike velocity, but to promote comparison, an area of 1m2 has been assumed for all machines.
This graph shows the road speed corresponding to engine speed in each of the gears. It is a function of the engine speed, primary gearing, gearbox ratios and final gearing. It also takes into account the effective wheel radius - which accounts for tyre loading and deformation.
The author's Sprint ST dyno run has provided an empirical value for the effective radius of the wheel, which has been applied universally. Different tyre sizes and aspect ratios have some effect here, but reliable data are not available.
This graph is a product of the Tractive Effort cadence chart.
It shows the net force available for maximum acceleration, i.e. it is the driving force less the resistance forces.
For simplicity, it is assumed that engine is held at max torque, and the clutch slipped off the line, maintaining maximum tyre traction. It is acknowledged that this contracticts what has been said earlier about optimal take-off, but it is simpler to engineer into the graphs, and there is no indication that road testers would have followed the max. power tako-off approach.
It is worthy of note that the Net TE curve is zero at the maximum speed.
The acceleration graph shows the result of applying the net tractive effort to the mass of the bike and rider.
In most cases, manufacturers only quote the mass of the dry bike. Ducati, exceptionally, quote the wet weight (without fuel). Mass of the rider can have a significant effect on the acceleration times, so please note when comparing data that the author's own data show the author's own mass - those of external tests use a nominal 90 kg rider.
The acceleration calculations make no allowance for tyre slip (beyond a nominal value) or of rotation (wheelies).
Acceleration data are summarised in the blue fields at the top of each sheet.
The author has only been able to get hold of one set of empirical acceleration data - those of the 1994 Triumph Trophy 3. Copies of any such data for the other bikes featured (preferably from a data logger) would be greatly appreciated.
The spreadsheets are designed to enable the reader to evaluate the effects on performance of changes in parameters such as: mass of the rider, mass of accessories, final drive ratio, etc.
For instant success, enter your 'ready to ride' weight (Mass rider), the weight of any accessories on your bike (Mass accessories), and the volume of fuel (Volume fuel) on which you want to base the information. The figures in pale blue give your acceleration times (in imperial units for ease of comparison).
NOTE: The acceleration graphs are hand crafted, and may require re-work if the power figures are significantly different from the original. The essence of the table is to move to the remainder of the next gear's tractive effort values when the TE of the current gear equals that of the next, adding the gear-change delay. To determine the cross-over rpm, select each gear's torque line on the Cadence chart, and note the point at which it crosses the line below (plot points are taken from the rpm values in the Measured Data table). The standard ST torque lines don't cross!
In addition to general texts on physics and mathematics, the following form my primary reference material: