In the 1950s, Grand Prix teams sometimes added the potency of nitromethane into their fuel mix for qualifying. IndyCar teams did the same into the 1960s. But these days nitro is only used in straight-line running, most notably by Top Fuel supercharged car and motorcycle engines. Our profile in RET 148 of the Harsh Top Fuel Motorcycle [TFM] vee twin prompted Heikki J Salminen to prepare this investigation into the power potential of such nitro engines for motorcycle and car racing.
Top Fuel Motorcycle vee twin (Courtesy of Harsh)
Engines are funny animals, writes Salminen (who has been closely involved in the development of the Harsh and before that of Puma TFM engines). Superficially, they look simple mechanical devices, but they have an outstanding talent for showcasing complex, hard-to grasp interactions. In practice, the complexity of interactions means that even with the best modern analytic tools available, engine developers still need to understand what they are doing. You can’t get rid of all the complexity, but there are ways of making simpler abstractions of intricate matters.
Top Fuel V8 (Courtesy of Kalitta Motorsports/TRD)
When you are working in a niche area such as TFM engines, one problem is the scarcity of data. There’s a bunch of engine builders and developers, and many of them are willing to share their experience. You may be happy following what others have done, and perhaps try to make incremental improvements to the base obtained from others.
That can be just fine for a racer, as races are normally won by crossing the finish line first and it does not matter by how large a margin. But should you not just want to go down the paths others have taken, you need to develop an understanding of the landscape in which you are moving. To get an overall picture of factors that affect the power from supercharged Top Fuel engines, a general understanding of engines serves as a guide, with help from dimensional analysis and similarity considerations.
Abstraction in exact natural sciences refers to the process of simplifying or distilling a complex phenomenon, system or concept by emphasising its essential features while ignoring less significant details. Dimensional analysis is used in natural sciences and engineering to analyse and simplify complex physical phenomena. It involves examining the relationships between physical quantities by considering their dimensions (such as length, time, mass and so on) rather than specific numerical values.
Dimensional analysis has been used to derive relationships such as the Reynolds number, which characterises the flow of fluids. That helps predict when flow transitions from laminar to turbulent, and is a critical factor in engineering design.
As mentioned dimensional analysis is an essential tool for abstracting complex physical phenomena, simplifying models and gaining deeper insights into the underlying principles governing these phenomena.
• Scaling: Dimensional analysis allows for the derivation of scaling laws, which describe how one variable depends on others. Such laws provide insights into the behaviour of complex systems and can help in making predictions and designing experiments.
• Non-dimensionalisation: Dimensional analysis can lead to the creation of dimensionless numbers, which are ratios of physical quantities with the same dimensions. They also make problems independent of scale, making it possible, for our purposes, to compare engines of different configuration, different size, different number of cylinders, in a way that makes sense.
• Simplification of equations: By expressing equations in terms of dimensionless variables, it is possible to simplify complex mathematical models. This makes it easier to analyse the behaviour of systems and gain insights into their underlying physics.
A first look in the real world with dimensions, considering similarities
1: Engine power
The amount of work (W) done by an engine cylinder over a working cycle is, as per definition: W = Vs · pme (1) That is, swept volume (Vs) times brake mean effective pressure (pme). Power from one cylinder (P1) is the work done by the cylinder times the frequency (f); P1 = W · f (2) Considering that cylinder swept volume is equal to the product of piston area and stroke, and mean piston speed is proportional to operating frequency times piston stroke, engine power (P) is proportional to the product of total piston area, mean piston speed and brake mean effective pressure: P ~ Ap cm pme (3) A bit lazily written, but if you want mathematical rigour, feel free to fill in the gaps!
2: Flow of air, and power obtained from the thermodynamic process
A very general view of engine power is obtained by looking at the engine as an energy conversion device. The purpose of thermal engines is to convert heat into mechanical power, a form of higher-ordered energy. The efficiency of thermal engines has an upper limit dependent on the ratio of temperatures at heat introduction versus heat rejection, known as the Carnot efficiency. An intensive quantity is one whose magnitude is independent of the size of the system. Now, let’s accept that we are dealing with machines that in terms of intensive quantities generate similar processes. In more plain language, they work so that the working medium goes through a similar succession of pressures and temperatures versus specific volume. The efficiency of the thermodynamic energy conversion process is determined by the intensive quantities
while the absolute amount of heat introduction is determined by the amount of fuel the engine is able to process, which again depends on the rate of airflow. The mass of fuel fed in, multiplied by energy released per unit of mass, times system efficiency is the power output. While Carnot sets a firm upper bound, practical efficiencies of engines representing a certain application do not vary wildly. Thus, airflow through the engine is the main power potential determinant – the very reason why superchargers are used.
3: Similarities
Assuming geometric and functional similarity of the engine’s thermodynamic conversion groups (individual cylinders in this context!) we can do with even simpler thinking. As a bonus, we can obtain a way of comparing performance potentials from different size engines and different numbers of cylinders. This should be useful for engine builders and motorsport rule makers alike. It can be shown by dimensional analysis that the level of mechanical stresses in similar engines is a function of mean piston speed only. For similar processes, brake mean pressure is the same, and in the big picture, largely independent of engine size. Consequently, the dependency of power output for similar engines can be reduced to: P ~ Ap (4) It just can’t get any simpler than this!
4: Different engine configurations and cylinder numbers
Now we all know reality is infinitely more complicated. Yet you can trust the principles based on similarity and dimensionality stated above, like you can trust gravity holding you onto the planet. For comparing different numbers of cylinders and engine configurations there are some simple relations to be found. If we consider a similar design of individual cylinders, in principle the mass of the cylinder-reciprocating assembly is directly related to the volume of the cylinder, as everything else scales up and down in all three dimensions. Disregarding the effects of cylinder arrangement – inline, vee, horizontal, radial or whatever – the total mass of the similar engine would only be a factor of the engine’s total displacement. However, power from similar engines would depend on total piston area only, as noted by equation (4) above. For similar engines’ power equality: Ap = const (5)
This is something used in the past as a basis for motorsports engine regulations. However, it tended to result in practice as strange engine configurations. In the field of large powerplant and ship engines, the common practice is to refer to engine type by cylinder diameter, as it reflects the engine’s power potential much better than displacement. In automotive use, it does make some sense that the amount of material used to make an engine is still pretty much related to the displacement, if not exactly, as is the build volume, and to a certain extent cost.
That is not to say that today’s normal ruling referring to total displacement would not be without its faults. One possible fault is that if the displacement was not used as the criteria, different stroke-to-bore ratios might be chosen, for example to arrive at the best possible power-to-mass ratio of the engine, or the best specific fuel consumption. Often the rules try to equate engines of different cylinder numbers (z). For this purpose, similarity laws offer a nice non-partial tool to be considered, for equal performance: V ~ z1/2 (6)
5: Engines compared
Reference: NHRA Top Fuel Dragster V8 500 cu in TFM engines:
Harsh V28 – Jaska Salakari’s revolutionary direct drive, digitalised vee-twin; world’s fastest in 1/8-mile (RET 148)
Suzuki I4 – generic engine with features roughly following Steve and Larry McBride’s world record-holding, multiple times US champion machine (RET 128)
Puma I4 – multiple times European championship machine boasting second fastest ET in the world (RET 58)
6: Parameters investigated
The standard ones:
Number of cylinders
Number of inlet valves per cylinder
Number of exhaust valves per cylinder
Bore
Stroke
Engine displacement volume
Inlet valve diameter(s)
Exhaust valve diameter(s)
Maximum engine speed
Supercharging related:
Supercharger swept volume
Supercharger drive ratio
Maximum supercharger speed
Supercharger volume flow @ nmax
Dimensionless values:
Stroke-to-bore ratio
Valve area as a percentage of bore area
Compression ratio
Compression chamber shallowness
Supercharger volumetric flow ratio
Inlet flow velocity ratio
7: Comparisons
Equalised cylinder displacements, similarity based:
The 1.7 litre vee twin is only equitable to a 1.2 litre four – so it is punching above its weight. Still, it fully packs the potential of the four-cylinder units, but in a lighter package.
The Puma I4 is clearly run in the lowest stressed state of all the engines in this comparison. The three-valve head and the longer stroke are advantages compared to the Suzuki I4.
8. Power potential based on air versus fuel flow
Power potential based on actual flow of fuel, as well as of air, was calculated. Instead of the commonly used air-tofuel ratio, a clearer picture is obtained by calculating the fuel equivalence ratio (f). Clearly all the engines depen mainly on the monopropellant property of nitromethane for power, as even the ‘leanest’ of engines is fed about three times the amount of fuel that could be burned.
The outstanding feature is that none of the motorcycle engines are operated under as heavy fuel load as the 500 cu in dragster engine. The TFM engines in this comparison are relatively equal. Any of the engines have the potential to be umber one with further development, as well as the potential of overpowering the chassis they are currently mounted in.
9: Verdict: Making sense of it
There were more parameters examined than could be reported in the time available for publication. However, this study has already revealed facts that were previously more or less hidden from the author. The greatest revelation is considered fuel load.
10: Conclusions
There is a big difference between the four and two-wheeled Top Fuel categories in drag racing. The former has a long history of stabilised technical regulation, as well as a large base of professional racers. Consequently, the practices of running the engines have become very refined, and the technology used is very mature. Within the framework of the rules, major improvements in performance seem next to impossible. Apparently, this is in accordance with the philosophy of the rule makers – trying to limit cost, taking care of safety, and making for an even level of competition. A side effect is that it takes away some of the technical interest in the sport.
TFM engines are the opposite. The base of competitors is not very large. There is an established engine configuration that is dominant, namely the inline four that traces back in history perhaps to the eighties. Whatever configuration is used, there is a lot of room to search for new solutions, whereas the existing ones are far from being fully exploited.
Appendix 1: Inertial stress, with similarities
A. Geometric translator and forces due to motion
Volume changes in a reciprocating piston engine are most commonly effectuated by a crank-con rod mechanism. There are some tweaks and design options considering this mechanism making the translation between reciprocating and rotating motion. The most important perhaps is the choice of rod-to-crank radius ratio. Piston motion is non-symmetric owing to finite rod length. However, scaling a design up or down, while keeping the geometric proportions the same, the acceleration pattern remains the same. The force acting on a volume of mass in an acceleration field is: F ~ a V (i) (mass density remaining invariant)
B. Stress due to force
Stress due to the mass force equals the force divided by cross-section: s = F/A (ii) (just omitting vector notation for simplicity, and because it is not really needed!)
C. Factors to consider
Accelerations at TDC and BDC depend on the rod ratio. The shorter the rod, the more non-symmetry there is; with a short rod, acceleration at TDC gets larger, at BDC less. For simplicity, let’s consider a very long rod. The absolute value of force required to keep the piston and rod following the circular path is then the same at both DC positions, and exactly the same as that required to keep the objects on a circular tract if the motion was purely rotational: F ~ m w²R (iii) Considering that m ~ R³ and A ~ R² and that for a similar design, piston stroke scales with the rest of the dimensions: s = F/A → s ~ R³ w²R/ R² → s ~ w² R² = F ~ m w²R (iv) Mean piston velocity cm is related to the engine’s rotational speed, as well as piston stroke, which again depends on crank radius R: cm ~ w R (v) We now see that in a similar engine design, the stress due to mass forces depends on mean piston speed (squared) only – independent of the size of the engine. s ~ cm² (vi)
Appendix 2: NHRA Top Fuel dragster: the reference engine
As per 2023 NHRA rule amendments, 20th release: 8/23/2023 SECTION 19: Top Fuel dragster, engine: 1, Engine (Page 2) (3/25/2023)
Any NHRA-accepted, reciprocating, 90o V8, single camshaft, automotive type engine permitted.
Multi-valve and/or overhead-cam engines prohibited.
Only one cylinder head design is acceptable:
Maximum two valves per cylinder Intake valve angle of 35o, ±1o
Intake valve size maximum: 2.470 in
Exhaust valve size maximum: 1.925 in
Exhaust valve angle of 21o, ±1o
Only one engine block design is acceptable
Engine size: 500 cu in maximum
Bore size: 4.1875 in, +0.004 in
Regarding the supercharger, the rules say: Roots-type: maximum size: 14-71
For Top Fuel and Funny Car, overdrive may not exceed 1.50 except in Denver, where 1.70 is the maximum. Swept volume of a 14- 1 Supercharger is 550 cu in
Comments on the tables
Stoichiometry
‘rst’ is short for stoichiometric ratio.
LHVs based on formation enthalpies at 25 °C are also shown on the table. Nitromethane combustion has two different stoichiometric combustion modes. The first one (Mode 1 ) in a 2020 study was said to be the prevailing one. What was not said is that the mode of combustion actually generates less heat than regular stoichiometric combustion of methanol, which also means it generates less power than stoichiometric combustion of methanol out of an engine. Going to a drag racing event, it is very easy to see that this does not apply to race engines. The engines are run nowhere near stoichiometric chemistry. That means simple combustion models are not able to characterise the situation.
Measurements
The screen of data from Don Schumacher Racing (DSR) shown in RET 90 (November 2015) obtained using the AVL torque sensing element exhibits oscillation of power around the reported power peak of 10156 bhp. The oscillation comes mainly from a variation of torque at roughly the running frequency of the engine. No explanation was given concerning the origin of this oscillation. Magnitude of the oscillation is roughly ±5% of local average. With no direct access to the original data, assuming this is the main source of inaccuracy, baseline average maximum power may be around 9600 bhp. Later, it was reported that on a second run the peak was 11051 bhp, which I would estimate to correspond to 10500 bhp , oscillations filtered out . Knowing that the measurements did not represent the ultimate maximum power available in 2015, I took the liberty of selecting 11000 bhp as the baseline. Puma I4 measurement was done on the layshaft. I took an approximate efficiency of 90% to account for power transmission losses. Even though it is real easy to write out lots of numbers from a measuring system, in practice achieving an absolute accuracy of even two significant digits can prove difficult.
Power calculations
The normal measuring methods include calculations: converting measured signals to units to be measured, and in the case of power measurements, multiplying the measured shaft speed with measured torque. The quality of measuring equipment, level of calibration accuracy, possible signal disturbance as well as methods used in data handling affect achievable accuracy. Calculations based on vehicle dynamics – acceleration and distance versus time – are even harder to calibrate, and at high speed, include hard-to-access components. If used for comparative purposes on one vehicle it is not that much of a problem, but one should be careful about claims on a more general level. For example, there was never even an attempt to seriously calibrate the on-the-run power calculations of Harsh V28. The calculation does agree with another calculation, namely the results of 1D power simulation, and we believe it is possible to make at least the values quoted.
Large power quotes get people’s attention, but in real life drag racing is about covering the distance as quickly as possible, and maximum power just for the sake of it is not even worth trying for.
Acknowledgements
Data thanks to Mitch Brown, Jaska Salakari, Marius van der Zijden, Timo Lehtimäki at TiL-Racing, Ian Bamsey/RET, and the NHRA 2023 rulebook.