This question can be answered with some basic physics.
There are two situations - (1) travelling on the flat; and (2) going up any kind of slope however slight.
Calculate/convert everything to JOULES (a measure of total energy) and WATTS (a measure of how much energy - joules - is being consumed or needs to be supplied per second).
(1) On the flat, each time you accelerate from zero or increase your speed you have to add Kinetic energy. Thereafter, some energy is required to overcome the rolling resistance of your bike/tyres and wind resistance but these are relatively smaller compared to the change in Kinetic energy. Unfortunately when you slow down, 99% of the kinetic energy is wasted/lost by conversion to heat in your brake linings. 1% may be 'recovered/usefully used' for overcoming air & tyre resistance during the de-acceleration period.
(2) Going up a hill/slope, you need to supply enough enough energy equal to your increase in Potential Energy relative to your starting height on the earth's surface. Unfortunately, when you go downhill, even if you freewheel rather than brake intermittently, you are still unlikely to convert more than a small proportion (<50%) of your accumulated Potential energy to Kinetic energy because of increased wind resistance etc during the speedy descent.
So, to actual numbers.
(1) Situation on the flat and level.
Kinetic Energy (in Joules) = mass (kg) x speed (metres/sec).
15mph = 6.7 metres/sec.
An 80kg man with 20kg bike accelerating from zero up to 15mph would need to supply 670 joules (100x6.7) each time.
Adding 5kg of milk, you would need 703.5 joules each time -- an increase of 5% in energy. Remember, everytime you slow down again, all that is lost.
With a 31kg bike and 5kg milk, the energy needed is 777.2 joules -- an increase of 16%.
https://www.chem.wisc.edu/deptfiles/genchem/netorial/modules/thermodynamics/energy/energy2.htm
(2) Going up a hill.
Potential Energy = mxgxh (where m=mass in kg, g=gravitational acceleration, h=height in metres).
g=9.8 m/sec/sec.
An 80kg man with 20kg bike going up a 1:10 hill at 5mph ascends approx 0.22 metres/sec (simple trig.) -- therefore energy needed is 215.6 joules per second (100x9.8x0.22).
1 joule/sec = 1 watt.
An averagely fit adult can sustain about 50 - 150 watts of work consistently, so you can see that to produce over 200 watts to go up a gentle hill is quite an effort. If the total weight is increased to 116kg (80+31+5), you need to sustain 250 watts -- another increase of 16%, but much more effort over accelerating on the level where one might normally take, say, 5 sec to get up to 15mph and requiring only 140 watts (703 / 5) during that 5 second period.
Going uphill requires almost 80% more effort (250 / 140) - whether supplied by man or man plus battery/motor - than
speeding up and slowing down on the level; ... and for a relatively gentle hill at that.
(3) As regards battery range.
The average 'standard original battery' is of about 300 Wh capacity.
1 Wh = 3600 joules. So 1,080,000 joules. But conversion inefficiency through the motor may optimistically only deliver no more than 75% of this -- so 810,000 joules available.
Potential energy required for lifting 100kg up a 50m hill is 49,000 joules.
Empirical estimates of energy consumption for air resistance etc at 15mph constant sped on the level is about 100-120 Watts -- ie. 120 joules/sec -- or about 432,000 joules per hour, not including de-accelerations/re-accelerations.
Depending on how much is supplied by you and how much is set to be supplied by your bike motor (50%?) -- one can work out how long/far you can theoretically go.
In practice, your own bodyweight has by far the most effect proportionately in most situations, but especially in hilly areas!
WR
