Sidepodcast - All for F1 and F1 for all

Tech Spec
Will Davies

Since before he can remember Will^ has watched F1 – he would always be sat down to watch the start before going out and continuing to follow on the radio. His first F1 memory is of his parents snoozing to what they considered the soporific tones of Murray Walker. Having lost touch somewhat during the years at university, Will^ has now reconnected with the sport and is a bigger fan than ever; often combining his interest for the more technical aspects with his love for maths for some 'interesting' results.

Flow rate gate - Projecting what might have happened had Red Bull played by the rules


Horner calling the shots on the Red Bull pitwall
Credit: Mark Thompson/Getty Images

Go with the flow

We all already know that Red Bull used their own fuel sensors (which contrary to their opinion is against the regulations), exceeded the maximum fuel mass flow rate, used their own interpretation of flow rate and deliberately ignored the FIA stewards’ mid-race requests to turn the rate down.

The regulations are fairly clear on the matter of fuel flow:

  • 5.1.4 Fuel mass flow must not exceed 100kg/h.
  • 5.10.3 Homologated sensors must be fitted which directly measure the pressure, the temperature and the flow of the fuel supplied to the injectors, these signals must be supplied to the FIA data logger.
  • 5.10.4 Only one homologated FIA fuel flow sensor may be fitted to the car which must be placed wholly within the fuel tank.

By the letter of the law Red Bull broke Article 5.10.4 by not having an FIA sanctioned sensor fitted to the car, so by extension broke Article 5.10.3 also. It is less clear to what extent Article 5.1.4 was broken as we’re not in possession of all the data.

It has been reported that Ricciardo’s car was delivering 25g of fuel more per lap than other cars, but there are some misconceptions floating around as to what that means. It doesn’t mean that he was using more fuel around the full lap rather that his engine was being provided with extra juice only during the moments of maximum throttle. 25g extra per lap equates to 1.45% extra, but we have to be careful about saying that he used 1.45% more fuel (by volume) than everyone else – it is clear he did not exceed the 100kg limit as he was not excluded for doing so.

Take leave of your sensors

Regular flow rate sensors will do exactly that, measure the speed at which fluid passes – as the cross-section of the pipe or tube is known, the volume of the fluid passing over a specific time can be calculated. But that is not what is used in this case; the FIA’s regulation governing fuel flow does not specify volume of fuel, the restriction is on mass of fuel per unit of time (100kg/h).

So, why is the use of mass-rate ‘interesting’? It’s interesting because it complicates things as mass is not proportional to volume, it is a function of density (school-level science tells us that Mass = Density × Volume). The density of liquids is not constant; it varies with atmospheric conditions – air pressure and temperature. Changes in density can mean that a fluids’ volume may flow at the same rate, but a different amount of mass may be transferred – an increase in density means an increase in mass flow rate, and a decrease will reduce the rate.

Mass rate sensors are not technically intricate in their construction. The fluid flows through a pipe which has a beam of ultrasound directed through it, but it is the way in which the sensors pick up the signals and interpret the results that makes these tricky beasts. There are two ways in which ultrasound can be used to calculate flow rates:

Option 1: The sensors measure the degree to which the frequency of sound changes as the beam reflects off particles in the fluid – for the technically minded they measure the Doppler shift. It depends whether the beam is directed towards or against the flow as to whether the higher the frequency of the returning beam means that the mass is flowing faster, or vice versa. This is measured in cycles per second (Hz).

Option 2: Two beams of ultrasound fire alternately, one is transmitted along the direction of fluid flow and another is transmitted against the flow, this is called the transit time method. The velocity of the fluid is a function of the time it takes the two beams to travel the same distance proportional to the time difference. The formula to calculate the rate of flow is given by

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Where L is the distance between the emitters/receivers, θ is the offset angle of the beams, t1 is the upstream time, t2 is the downstream time. It appears that in these sensors the two beams are fired at directly with/against the direction of flow, i.e. at an offset angle of 90°. As sin(90) = 1, the formula becomes:

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An exact value for the velocity can be achieved by calibrating the sensor against known parameters.

Calibrating the sensor is not a simple task. Sensors come from a single manufacturer and prior to each being used it has to be calibrated by a team contracted by the FIA (only sensors manufactured by Gill Sensors’ have been homologated, and it’s not the one whose sensor Red Bull used during the Melbourne race). It has to be calibrated using the specific fuel each team will use, in a variety of conditions and at five different temperatures. A range of calibrations needs to be made in order to sample the signals from each sensor when the density of the fuel is different in these differing conditions. Differing densities means that beams of sound waves will travel at a different speed through the liquid, so would make it appear that the mass is travelling at a different rate than its actual velocity. Each sensor is designed and built to measure flow rates so that temperature, pressure and motion (including G forces and heavy vibration) do not affect the accuracy of the readings. This only means that the sensor’s readings are independent of external influences, but not that the sensor can account for the effect those conditions have on the fluid.

Although a large variety of conditions have been tested, this does not take into account the natural variance during a race weekend. It is likely that the teams are actively managing their fuel flow, down to the point that they are inputting real-time temperature and atmospheric pressure into their control systems, in order to maximise their fuel flow and hence their performance. Pushing the envelope in this area may not be what the FIA had expected to happen and as they are likely using a single calibration set-up for the race; a ‘legitimate’ change by a team could push their calculation for flow rate above the rate as calculated by the FIA. This would happen if teams adjust their fuel delivery because the atmospheric air pressure decreases or the temperature rises; both of these will decrease the density of the fuel as it expands – less weight will be contained in the same amount of volume.

A sensor's life span is usually 400 hours and they need recalibrating after 100 hours of operation. With complicated pieces of technology, comes an increased likelihood of failure. When this happens they can provide inaccurate readings (high or low) or just transmitting/receiving can fail completely. In which case it is only the data logging aspect that is lost, the flow of fuel to the engine is not impeded and the car will continue to run as normal, but without anyone able to see the fuel mass flow rate in real time. There are fall back methods to calculate mass flow, and will typically involve using the velocity (and hence volume) that the fuel is flowing into the engine, together with its density. Placing the sensor inside the fuel tank is not necessarily a good idea for a part that is apparently prone to failure, but then that is what the FIA decided.

A major issue as I see it is that teams may be adjusting the flow rates in real-time to compensate for weather changes

It appears that the Red Bull engine was using a maximum of 1.5% extra fuel per lap, which they allege is within the tolerance of the sensors, but a working sensor is built to be better than ±0.25% accurate, so assuming the sensor was working correctly then 1.5% is quite a bit larger – “assuming” being the operative word. To try to combat the inaccuracy of readings and iron out any teething problems, the FIA reduced the frequency that measurements were taken from 10Hz down to 5Hz. Taking measurements half as frequently might go some way to increase the margin for error, perhaps to a point that the Red Bull reading falls close to or within it.

A major issue as I see it is that teams may be adjusting the flow rates in real-time to compensate for weather changes, whereas the FIA fix the atmospheric conditions variables at certain points during the weekend.

  • 6.5.2 [...]When assessing compliance, the ambient temperature will be that recorded by the FIA appointed weather service provider one hour before any practice session or two hours before the race[...]

The problem being that any changes the teams make to their fuel flow to cope with the changing conditions does not look to be legal. In an ideal world the FIA needs a tank of fuel (from each supplier) sat in the paddock during qualifying and the race that they actively measure the density of, then feed this to the teams in real-time. Then the teams can actively manage the flow rate of their fuel, optimising it so that it can deliver a maximum of 100kg/hour independent of fluctuations in density.

At the end of the day, not racing with a homologated sensor and ignoring the FIA during the race is probably enough to have the disqualification of Ricciardo’s Red Bull upheld. But that doesn’t combat the underlying issues that the sensors are clearly not reliable enough for some teams that want to eke out as much as possible from the regulations and the regulation is not as concrete as it first appears. (We might get a glimpse behind the scenes of the FIA’s current processes and get a better insight into the application of the regulations in the fall out of the protest hearing.)

Ebb and flow

Ricciardo's happy with second place in Melbourne
Credit: Vladimir Rys

So, what ‘should’ve’ happened if Ricciardo’s car had been running within the regulations? A lap around Melbourne is a shade or two over 1 minute 30 seconds which equals 2.5% of an hour. At the maximum flow rate of 100kg/h an F1 car would consume a maximum 2.5kg over the course of a lap.

Scenario A: If the Red Bull(s) were running as has been reported, such that they used 25g more per lap than other cars on track, this equates to providing the engine with 1% more fuel to play with per lap.

Assuming that 1% extra fuel meant over the course of a lap the engine produced 101% as much power as others, then Ricciardo’s race would have taken him 100/101 (≈99%) as long as it should have. (This is of course if we ignore other factors such as specific choices by the team to cruise the last few laps somewhat.) Dividing his total race time (1 hour 33 minutes 26 seconds) by 99% will project his total elapsed time (without the extra liquid-help).

93:26/99% = 95:22 (which is 57s slower)

If Ricciardo were to have finished 56s behind where he did, then he would’ve been somewhere around 7th or 8th, with Kimi Räikkönen breathing right down his neck (there would’ve been less than a second in it). Of course if Dan had actually been mixing it in the middle of the pack then he would likely have been even further back. A lot of effort is spent and time is lost when driving in close proximity to other drivers, so could’ve conceivably slipped as far back as Kvyat in 9th, a further 6s back.

Scenario B: Elsewhere it is reported that going above the 1% over the maximum flow rate for 10s equates to an extra 3g of fuel, so if the Red Bull(s) used as reported 25g too much, then this is a whopping 8.3% over the course of a lap. This boils down to an extra 83.25s on top of his finishing time, putting Pérez in 10th hot on his heals.

Enough of the speculation, one thing is certain, Daniel Ricciardo wouldn’t have done as well as he did if his car was actually running within the rules, and he is unlikely to get the points back for his “first podium”. But what is also clear is that there are teething problems with the newly introduced technologies, ones that need resolving one way or another, sooner or later.