I’ve used a gasoline lawnmower over nearly 3 decennia and I’ve been fed up with changing the oil, cleaning up the spark and the air filter, fetching gasoline in the jerry can, filling the tank, pulling the cord to start it up and furthermore I’ve also been disappointed by the evaporation of the gasoline remaining in the tank after mowing.
But above all I’ve been still more concerned with the greenhouse gas (GHG) emissions. So, since a couple of years I’ve been scrutinizing the lawnmower offers for an adapted and affordable battery powered lawnmower, thus an electric one which does not need a cord for its electricity supply. Of course, electricity available from the grid, is also not exempt op GHG emissions, but they are much lower (at least reduced by a factor 4, see further).
My garden has not got a so large area (roughly 600m²) but is quite long (around 60m in its longest side) and several ‘obstacles’ encumber its surface, like small fruit trees, playhouse, slide.
Looking to new offers, I have often been surprised by the area adequacy some lawnmower manufacturers dare to claim, which seems more than once much overstated.
But ‘seem’ is not an acceptable statement for an engineer. I have to be sure, or at least technically convinced. If I decide to buy a defined lawnmower, and not another one (which can be cheaper), the autonomy of the battery (accu) must match the requirements.
And which are the requirements ? A first answer is to enable at least the mowing of an area that is 10% larger than the one I have to mow, with the provided accu(‘s). Another answer could be nearly the same, but with additional accu’s that I could charge between 2 consecutive mowings. For instance, in case of a weekly cut, which is very common in season, 7 accu’s by charger could be an option, assuming a charging time of several hours so that each day (night indeed) another accu can be charged, providing 7 charged accu’s at the start of the lawn mowing.
The analysis could go further and envisage several chargers, but this is not realistic. The cost of accu’s and chargers are so expensive that the business case sinks when more than 1 additional accu set is necessary. I used intentionally the locution ‘accu set’, because some lawnmower are sold with more then 1 accu and among them some have got a housing in the machine which can host 2 accu’s.
So, back to the first answer, the requirement is an autonomy equal to 10% more than the area to mow, with the provided accu set. Now, let us have a look to the kernel of the discussion, how can I calculate this autonomy, since relying on the manufacturers to present correct figures is rather risky ?
Well, the best think is to start from what you know. And what I know is how much gasoline my lawnmower burns for each cut.
Most of us do not know this figure. So I did, till I measured it, at filling. This was an iterative path, because the tank must be empty at the end of the mowing, otherwise you need to recover the remaining fuel, which operation is quite uneasy and unprecise (loss of the unmeasured quantity that is spilled).
But once, known, this volume of gasoline can be converted into an amount of energy, using its GCV (gross caloric value). However, this amount of energy is not the one an electric engine will need. In fact, the gasoline motor is characterized by a (thermal) yield (squeezed by the Carnot losses and the technical losses), which is far (below) from 100%. If this yield was of 20% while the one of an electric motor was of 80%, this last one would consume ¼ (20%/80%) of the GCV energy burned by the gasoline (internal combustion) engine (ICE).
So I had to estimate (sharply enough) the yield of the gasoline motor of my lawnmower. When you will try to do it for your own, take care of being sure of the figure you will use, otherwise you will get a wrong dimensioning for your accu. The calculations presented below are adequate in my case and it is not sure they are applicable for any one.
Because I do not have a test bank at home, and it would be too expensive to ask a yield metering to a professional lab, I had to turn to estimations.
Applying the theory of the ICE to compute the yield would require detailed technical information about the thermal cycle followed by the engine (p – v diagram). But such information is not available. On the contrary, the yield of small mobile power generators (like the ones used in some booths on street markets) is common information for most of them.
Of course this figure is given for the best operating conditions (it is also a commercial argument), thus it is the upper limit for the actual yield. These conditions will be matched when the motor will have reached its operating temperature (thus after 60 to 80 minutes rotating at nominal, or rather optimal, speed).
It is clear that a lawnmower will be operating at a lower yield level. So how to calculate this level ? Well modelling the yield in function of the motor temperature and the motor speed is not so difficult. The temperature dependence is a kind of (exponential) saturation curve (like Y . [ 1 – e-t/T], where Y is the maximum level asymptotically approached, T the characteristic time laying around 15-30 minutes for thermal processes, and t the elapsed time since the engine’s start). The rotation speed dependency is a strongly flattened parabola, so that it could be replaced by a line (like Y = a . r + b, with a and b constant and r being the rotation speed).
The maximum yield for mobile generators delivering an output power in the range of my lawnmower (3 to 4 HP, thus 2,1 to 3 kW) lays around 20% (at the maximum). The torque curve of such a 4 strokes engine is quite flat between the lowest and highest (accessible) operating speed, thus the ‘r’ term in the formula above is much smaller than the b, resulting in a yield varying between 75% and 100% of its maximum.
Since the motor of my lawnmower runs mainly just above the idle speed during the mowing, I have to take 80%. Since the duration of a mowing is around 80 minutes and T (the characteristic time of the motor warming up) is rather of 30 minutes (due to low rotation speed, because of operation near idle), I have a global yield of 12% (average from integral of saturation curve with Y = 20% ´ 80%, which is 16%, t being 80 minutes and T being 20 minutes).
With a GCV of 43MJ/kg and a density of 0,73 kg/l thus 8,7kWh/l, a volume of 0,3l of gasoline frees up 2,61 kWh (9,4MJ) with a global yield of 12%, which leads to a necessary energy of 313 Wh (0,313 kWh or 1,13 MJ). This is the energy figure I used to verify whether the provided battery (accu’s set) is sufficient.
The lawnmower I selected have got 2 accu’s (provided with the machine, which has got a housing for both, while the charger can only host 1 accu), each of 4Ah capacity, deliverable at a voltage of 40V. The corresponding energy is thus 2 (accu’s) ´ 4 (Ah) ´ 40 (V) = 320 Wh (since 1 A ´ 1 V = 1 W and 1 W ´ 1 h = 1 Wh).
The provided accu’s are thus just sufficient (2% margin), so without any other actual spare than the possible overestimation of the yield of the ICE of my old lawnmower. Although, I have the possibility to buy 1 extra accu to get 50% more energy, which will be more than enough.
I bought it thus, knowing that I incurred the risk of need of an additional accu. The very first time I mowed, I have just been able to cut 65% of the area. I was abashed, but did not give up and, surprisingly, the second time (and all the following ones) I could achieve the mowing of the entire surface, sometimes with still a little bit margin (remaining energy in 1 of the accu, the mower using the accu’s sequentially and not in parallel).
I guess the batteries were not properly charged by the first mowing, however I checked their charging state before. I learned later that, the first charge could not be optimal, but did not receive an explanation for the phenomenon in behind. A new path of investigations opens thus … for another article.
Anyway, lawn mowing with the accu device is fine, quite, easy (the machine is lighter) and I have no more to go to the tank station to fill the jerry can (but well to charge the accu’s) neither to pull the cord, clean the spark, clean the air filter. And, above all, I reduced the my CO2 emissions as well as the evaporation of the remaining fuel at the end of the mowing.