2.1 The problem of battery-electric aeroplane take-off performance

The problem of measuring and scheduling take-off and initial climb performance for a conventional aeroplane is extremely well understood and widely published upon. However, a battery-electric aeroplane introduces additional parameters not normally considered. These are particularly SoC and TAFT (time at full throttle). It is likely that SoH (state of health) must also be considered in the future as this programme was flown entirely with a relatively young powertrain with components in new condition. Existing parameters of wind, weight, slope and density altitude remain significant. However, it should also be considered that whilst density altitude effects upon airframe and wing should be unchanged compared to a conventional aeroplane, impacts upon a motor/propeller combination are such that whilst propellers will still be influenced by density effects, power source output should be unchanged, with the exception of air cooling/heat transfer and the consequent impact of air temperature upon system operating temperatures.

2.2 The test aircraft

The aeroplane tested in this programme was the Sherwood eKub (Fig. 1) registration G-EKUB, which was built as part of the EnabEl: Enabling Aircraft Electrification project, and is a first-of type derivative of the established Sherwood Kub single seat tailwheel high-wing single thrustline aeroplane, built by The Light Aircraft Company (TLAC) – see Table 1. The aeroplane is powered by five 3.5kWh 57V Lithium-ion battery packs, powering via an air-cooled inverter, a Geiger Engineering HP20 three-phase air cooled motor, and eProp CFRP ground adjustable two-blade propellerr. Carrying through from batteries to motor, are five sets of parallel DC cabling into an inverter inlet bus-bar, the 28kVA DC to 3-phase inverter, then parallel 3-phase cabling from inverter to motor (Fig 2). Independently conducted flight test articles on the aircraft can be found at Refs [Reference Unwin20, Reference Unwin21]. Whilst design analysis favoured a three-battery system as the most design efficient solution (more giving greater system mass, less giving insufficient excess power to reliably permit a go-around in the event of a single pack failure), the choice to use a five-battery system was driven by availability of suitable commercial off-the-shelf (COTS) components within the project timescale. The batteries, massing 15.5kg each, were located two in each wing root, and one in the nose between the motor and firewall; battery locations were driven by the combination of available space within the airframe and the need to maintain centre of gravity within limits.

Figure 2. Sherwood eKub powertrain schematic.

At time of writing, G-EKUB has flown 31 sorties, totalling a little over 20 flying hours. The greatest endurance actually demonstrated has been 54 minutes from take-off to landing, and the greatest altitude demonstrated has been 6,300ft above airfield elevation.

2.3 Instrumentation and consideration of errors

Automated data recording was available from (a) SkyDemon flight planning application recording GPS data at 0.2Hz; (b) the Geiger Engineering ADI (advanced drive interface) unit fitted to the aircraft’s instrument panel (Fig 3). Manual data recording was by the test pilot, who had reference to normal flight instruments, the ADI unit’s display, and also a uAvionics AV30 mini-EFIS [22] (electronic flight instrumentation system) fitted into the aircraft’s instrument panel – incorporating digital solid state direction indicator and attitude indicator, as well as additional indicated airspeed and pressure altitude. Timing was by reference both to SkyDemon automated recording, and a synchronised personal chronometer.

Figure 3. Sherwood eKub’s instrument panel. Left to right showing eSTOP emergency powertrain control, battery management panel, AV30 mini-EFIS, altimeter, cockpit thermometer (above), turn co-ordinator (below), airspeed indicator, ADI unit, VHF radio.

Ground and local weather conditions were determined by observation, using a calibrated 15kt windsock [Reference Gratton23] at the Little Snoring test airfield, and the official Meteorological Observations from a nearby military aerodrome, RAF Marham (20nm to the North, with very few obstructions or changes in terrain between the two thus also considered a good representation).

It was assumed that measurements of temperature (air temperatures and system components) were exact within reading precision. SoC was calibrated in ground test detailed below, and the pitot-static system had been calibrated in previous flight test using the GPS racetrack method. Reading precision of instruments was ±1°C for temperatures (assumed exact), ±2mph for airspeed (previously calibrated against GPS), ±10ft for pressure altitude (presumed exact over the small distances between ground and circuit height), ±0.1kW for power (presumed exact). Measurement of take-off distances using GPS (descriptions below) was precise to ±10m in the horizontal plane and ±2m in the vertical axis with GPS data otherwise assumed to be exact.

2.4 The concept of TAFT and why do we think it matters?

TAFT is a new concept which was identified early in this programme as the powertrain was integrated and tested on G-EKUB prior to first flight. It was observed with the early, powertrain prototype, where ground testing showed that after selection of full power via the aircraft throttle (a potentiometer on the left hand side of the cockpit, feeding a signal to the ADI unit and thence to the inverter) that initial power reduced markedly with time. For example Table 2 shows the results for an early test at full throttle, where SOAP (the maximum available power available at any moment) drops off by over 10% in the first minute. Motor temperature appeared to be a factor in this, and that was emphasised during early test flying where it was found that initially available climb performance degraded rapidly within the first few minutes of a flight.

Table 2. Sample full throttle test (pre first flight, 20 Dec 2021)

This motor temperature effect – both impacting performance and safety became deeply problematic during early flight testing, to a far greater extent than predicted at the design and ground test phases, as illustrated by a six-minute performance climb from take-off through a throttle retard to keep temperature down to 18kW at 1 minute, until the throttle was further retarded to prevent motor overheat at six minutes in Fig. 4. This shows a marked drop-off in climb performance with time at a fixed throttle setting, despite relatively small changes in altitude: see Table 3; the inevitable conclusion was that the major player was motor temperature. It was also a critical point in the flight test programme where it was concluded that the aircraft’s motor cooling capability was inadequate to the task as the degree to which the test pilot was having to manage throttle setting and airspeed was unacceptable, leading to a five-month pause in the flight test programme whilst the cooling system was redesigned, tested and authorised for a return to flight.

Figure 4. Sherwood eKub climb performance from take-off, sortie 14, 30 June 2022 (runway elevation approx 1,500ft sHd) test pilot observations.

After the aircraft’s return to flight in November 2022, the motor temperature was now continuously below 65°C irrespective of powertrain handling, keeping it well below the programme target limit of 85°C and the system auto-retard condition of 95°C. Climb performance, with no other changes to the aircraft and powertrain except for improved cooling, was about 20% better at identical conditions and a continuous full throttle climb was demonstrated through over 6,000ft. This reinforced the conclusion that motor temperature was a critical factor in determining SOAP, however it was still found in a new series of ground tests that there was a drop-off in SOAP which was not solely explainable from reducing SoC or from temperature – see Fig. 5. These tests, apart from the first at 101% SoCi (from 30°C) were all done from 50°C motor temperature and if, for example, the data for the 55% and 44% commencing SoC cases are considered it can be seen that at throttle retard after five minutes where full throttle power was 19kW, this recovered after about four minutes at idle (∼200W) power to permit 19.8kW at full throttle. Motor temperature may have been a factor still: at the end of the 51%SoCi test T_M=62°C, at the start of the 44%SoCi test T_M=50°C) but it was also observed that the battery system voltage which had steadily dropped whilst discharging at high power, exhibited a significant recovery during the intervening four minutes at low power: the behaviour indicates that voltage, and voltage recovery is also therefore a TAFT contributor in addition to motor temperature. This is illustrated in Fig. 6, where the voltage drop during high discharge, and significant but not complete recovery of voltage at low discharge is very clear.

Table 3. Critical factors during sortie 14 climb

Figure 5. eKub power versus TAFT during ground tests on 10 July 2023.

Figure 6. eKub battery system voltage against time, during conduct of ground test shown in Fig. 5.

It is considered likely that inverter operating conditions and recent history may also influence TAFT effects. This is emphasised when considering the curve of total available power versus system voltage shown in Fig. 7 – demonstrating behaviour substantially the same as have also been seen in tests with only four of the five battery packs serviceable. Therefore voltage is confirmed to be only part of the position. However evidence towards (or against) that proposition is not available from this programme due to the generally very consistent self management of temperature by the inverter unit fitted.

Figure 7. eKub/Geiger powertrain available maximum power as a function of system voltage.

The conclusion therefore is that TAFT is an important parameter in determining SOAP, and is a function of at least two internal parameters: motor temperature and system voltage, and likely in some aircraft at least a third – inverter temperature, and potentially a fourth – internal system logic. At a first approximation however it seems reasonable to assume that Equation (1) applies to any system.

(1) \begin{align}\mathrm{SOAP} = \mathrm{f}(\mathrm{SoC})-\mathrm{k}.\mathrm{TAFT}\end{align}

The function f, and value of the multiplier k are unknown. By inspection of Fig. 5 we may however conclude that SoC as an indicated value is not an accurate descriptor of total energy reserves in this aeroplane at least (given that after initial charge SoCi=101%, and from 0%, the motor could operate for another five minutes at about a mean of 11.5kW, giving residual energy of about 1kW or about 6% of the system declared capacity). In other words f(SoC)≠ SoC. If one assumed linearity between true and indicated SoC, in percent, which is probably reasonable, we can conclude Equation (2):-

(2) \begin{align}\mathrm{SoCt} = \left( {0.931\ \mathrm{SoCi}} \right) + 6\end{align}

(Both parts of the equation in %).

This clearly only applies to this individual aeroplane and system, but is a useful working relationship for purposes of flight test data analysis, and indicative for other projects of the form of relationship they may encounter.

3.1 Actual take-off distances

Ultimately, irrespective of ground testing and theoretical analysis, aeroplane performance can only be determined accurately by actual flight test. The eKub is a test aeroplane, and has been used therefore to obtain such data; whilst many other flights for a range of systems, performance and handling evaluation have been made, the primary flight used in this paper was eKub sortie 30, flown on 26 July 2023 when a series of nine circuits were flown from the hard section of runway 25 at Little Snoring Aerodrome in Norfolk, UK (Fig 8). Wind was 8kts at 240° (in conformation of which all tests were at 55mph IAS = 47.5kts CAS = 48.2kts TAS = 48kts groundspeed component when corrected for an average 5.7° climb angle as they climbed through 30ft where wind is conventionally measured. The mean of those tests was a groundspeed of 38.8kts; 47.5 – 38 = 9.5kts windspeed at 30ft – close to the observed 8kts but the higher figure was used for subsequent calculations), air temperature was 19°C, air dewpoint was 11°C, surface air pressure (QFE) was 1003hPa: giving a density altitude of 1,060ft. All take-offs commenced at the start of the hard section of runway 25 (landings subsequently on the earlier grass section). Take-off distances were determined using automatically recorded data by SkyDemon [24] on the pilot’s in-flight personal device, which was then analysed using Google Earth (Fig. 9).

Figure 8. Little Snoring Airfield (from Pooleys UK VFR Flight Guide 2023).

Figure 9. Google Earth analysis screen showing full sortie data.

The data were obtained by the test pilot (raw data obviously provided IAS, not CAS, but the Pitot-static system had previously been calibrated using the racetrack method [25] – the calibration curve is shown in Fig. 10, based upon previous flight testing), in addition to the automatically recorded data from SkyDemon. After take-off the aeroplane was always climbed straight ahead to 300ft AGL, when a right-hand turn was commenced through 90° heading change followed by a second right-hand turn approximately parallel to the runway at 400ft. The aeroplane was levelled at 600ft (requiring 13–14kW), and then two descending right-hand turns before a low powered descent to land on the grass runway segment (in piloting terms, approximately a standard right hand 600ft circuit; the relatively low circuit was flown to permit more circuits to be flown with the energy available).

Figure 10. Sherwood eKub airspeed indication system calibration curve. Curve shown is lowest order (quadratic) best fit within ±2mphIAS precision, limited extrapolation below test speeds to clean stall.

As was expected, with reducing SoC, take-off run (TOR) and take-off distance (TOD) both increased. The full analysed results for actual conditions, with best fit quadratic curves (limited extrapolation from tested 37% SoCi down to 17% SoCi shown) are given in Fig. 11 with equations in the tested conditions for TOR and TOD. What may be particularly observed at this stage is the marked increase in distances as the battery state of charge reduces.

Figure 11. Sherwood eKub Take-Off Run and Take-Off Distance at Density Altitude 1,060ft with 9.5kt headwind. Nominal quadratic best fit curves with limited extrapolation to lower SoC below test conditions.

3.3 Defining minimum state of charge for safe take-off (SoC_MTO)

A problem identified during this project, and indeed which appears to have been identified by other projects such as the world’s only certified electric aeroplane the Pipistrel Velis Electro which carries a cockpit placard prohibiting take-off with less than 50% SoCi, is the question of what what point does the degrading SoC become such that a take-off should no longer be attempted. One approach of course is that the data such as has been described and shown above should be provided, with which pilots are then equipped to make their own rational decisions based upon their trained skill and knowledge. However multiple precedents exist, including in BCAR Section S⁽²⁷⁾, the UK’s airworthiness standard for microlight aeroplanes, which requires at S65 Climb that “The time for climb from leaving the ground up to 1,000ft above the field must be determined and when corrected for sea level, must not exceed four minutes”. Similarly, in CS.23², which is the airworthiness standard that would apply to larger aeroplanes it is a requirement of CS.23.65 that “Each normal, utility and aerobatic category reciprocating engine powered aeroplane of 2,722kg (6,000lb) or less maximum weight must have a steady gradient of climb at sea level of at-least 8.3% for landplanes”. Both contain further qualifying instruction, that aren’t relevant to this project. A climb gradient of 8.3% corresponds to 4.74° climb angle. Therefore it was considered appropriate to recommend that climb rate from ISA sea-level to 1,000ft, and climb gradient are both determined and that for microlight aeroplanes (up to 600kg MTOM and 45kts V_SO) the first requirement should determine minimum SoC for take-off, and for light aeroplanes (exceeding 600kg MTOM and/or 45kts V_SO, up to 2,722kg and/or 61kts V_SO for single engine aeroplanes) the sea level climb gradient should inform the minimum SoC for take-off. This is the recommendation of this paper, and was the internal decision made for the Sherwood eKub but, at time of writing, is not incorporated in any regulations.

Before proceeding with this, it was helpful to confirm that the aeroplane was capable of meeting such requirement at-all. In sortie 18, flown on 17 January 2023 the aeroplane was climbed at 625lb (95% MTOM), OAT-3°C (ISA-18), QFE 978, with an initial 100%SoCi from 1,000ft sHp (surface level at 1,013hPa) to 7,240ft (end of climb 35%SoCi). Reducing to standard density altitude, and extrapolating down to sea-level using a quadratic best fit, this gave the results shown in Fig. 13. The aeroplane started at a take-off from -970ft sHd and 100% SoCi, and climbed through 0ft at about 91% SoC, with the subsequent 1,000ft climb being performed in 3.1 minutes, comfortably exceeding the minimum requirement.

Figure 13. Sherwood eKub climb performance at full throttle, from -970ft standard density altitude. Best fit quadratic curve to raw data recorded by test pilot.

The problem then is of scaling this to varying values of SoC without having to perform multiple performance climbs. This was done by scaling from the SkyDemon obtained flight test data, using the time to 300ft, which was a convenient marker as it was take-off until immediately before the first turn. At first approximation we were able to fit a linear fit to that which was that RoC from runway to 300ft was RoC = 2.841SoC_I+174 feet/minute. Scaling that linearly to the time to 1,000ft (compared to the 90% SOCi at t=0 result in Fig. 7, this gave the result in Fig. 8, from which the conclusion is that the aeroplane can meet the 1,000ft initial climb requirement at or above SoCi=57% (Fig. 14). The decision for this aeroplane, for which microlight regulations are most appropriate therefore was that in the manual and on a placard the words “Take-offs not recommended below 57% SoC” would be included. (This corresponds to 59% SoCt.)

Coining a term for this, SoCi_MTO=57% for compliance with BCAR Section S

Table 4. Raw cockpit recorded flight test data

Figure 14. eKub standardised time to climb from 0 to 1,000ft standard density altitude.

Treating the eKub alternately as if it were a part 23 aeroplane up to 2,722kg however requires slightly different treatment. Using the mean climb rate from 0 to 1,000ft sHd, and the eKub’s best climb speed of 45kts CAS, a climb gradient chart is readily plotted; time to climb is shown in Table 4 and Fig 13, and then a derivative gradient chart in Fig. 15. Based upon this, were this a part 23 aeroplane, with the requirement that the climb gradient at standard conditions should be not worse than 8.3% the minimum SoCi for take-off would be 72% (corresponding to 73% SoCt). This is a large value, but not an unrealistic one – given that electric aeroplanes are inevitably limited in total capacity in any case (the eKub has demonstrated, flown economically a total endurance of 70 minutes without reserves, and this may make it one of the best aeroplanes in the world in that regard), and save for training circuits it is unlikely that many flights would be launched with a lower state of charge.

Figure 15. eKub standardised climb gradient between 0 and 1,000ft sHd versus SoC_I.

Applying the same term as above, SoCi_MTO=72% for compliance with part 23.