Solar Centipede – Part II – Solar Energy Calculations

 

 

In the Solar Centipede – Part I, the solar energy captured was a very crude estimate of 205 w per hour from a 340 w top mounted panel and 2 x 100 w panels on either side of the carriage mounted vertically.

In order to get a more accurate calculation of the performance of the vehicle, it is necessary to more accurately model how much energy the vehicle has available to move.

Online Solar Panel Calculators

National Oceanographic and Atmospheric Administration

National Renewable Energy Laboratory Calculator

Solar Electricity Handbook Solar Radiation Calculator

Details for Calculation

Alice Springs, Australia (-23.69748, 133.88362)

Efficiency of Panel = 17.5% (340w panel on Alibaba)

Top Panel – Average Solar Radiation Per Day/M^2, per Month of Year, for top panel facing upwards = 5.25 kw/h

Top Panel Available Energy = Total Radiation * efficiency * area = 5.25 * 0.175 * 2 = 1.83 kw/h per day

Screenshot 2018-01-27 at 11.01.42

Side Panels – Average Solar Radiation Per Day/M^2, per Month of year, for assuming average orientation of 45 degrees = 3.25 kw/h

(At there are panels on either side of the vehicle, we can assume the average orientation is 45 degrees)

Side Panels Available Energy = Total Radiation * efficiency * area = 3.25 * 0.175 * 0.8 = 0.455 kw/h per day

Screenshot 2018-01-27 at 11.02.30

Total Average Available Energy in Alice Springs = 2.285 kw/h per carriage (Yearly Average Speed over 24 hours would be, 38 km/h) (Yearly Average Speed Math)

Mid Winter Solar Captured Value = 1.91 kw/h per carriage (Winter Average Speed over 24 hours would be, 28km/h) (Winter Average Speed Math)

Mid Summer Solar Captured Value = 3.26 kw/h per carriage (Summer average Speed over 24 hours would be 55 km/h) (Summer Average Speed Math)

Solar Centipede – Part I

drone with car

 

*caveat* I don’t have any mechanical engineering, automotive etc experience.
Feedback on anything I’ve missed or gotten wrong is welcome!

Scenario

There are two locations roughly on the equator, with a 1,000 km road between them. Both locations need to send 5,000 kg of goods between them every second day. Each location has no resources. The vehicle that travels between them must be completely self-sufficient in energy.

  • Distance to cover in 24 hours is 1,000 km (41.76 km/h)
  • Cargo load to carry 5,000 kg, with an area of 25 m^3
  • No traffic, so no collision avoidance required
  • No restriction on vehicle size
  • Vehicle must not require external sources of energy
  • The route is completely flat with no elevation change
  • There are no clouds or other impediments to sunlight
  • There are no cross winds
  • The road does curve, but a tight turning circle is not required
  • It will move 1,800,000 kg of goods per year, over 540,000 km
  • The scenario starts at dawn, with no residual energy stored (batteries etc are empty)
  • It’s assumed components don’t suffer degraded performance due to wear
  • It’s assumed a self driving system can run on a low speed vehicle at 50w

Design Considerations

  • Solar is the only source of energy. We need to optimise for its collection
  • Aerodynamic drag will be a major consumer of this scare source of power. Optimising to minimise it will be crucial
  • There is a time limit to when the destination must be reached. This means there will be a trade off in the most efficient speed to move over a 24 hour period balancing aerodynamic losses and losses of storing energy
  • Keeping the vehicle lightweight will be important
  • To keep costs down, the design could be modular to maximise the repeat ability of construction
  • A long vehicle, with a low coefficient of drag and a minimal frontal area will be the key to effiency

The Solar Centipede

whole 2

  • Proposed solution to this problem is a modular carriage system consisting of 24 identical carriages, joined end to end. 1 m wide, 55 m long and 0.5 m high.
  • It has a single front specialised aerodynamic carriage that is heavier and has more powerful motors
  • Unlike a train, where an engine carriage is pulling the carriages behind it. Each module is overcoming its own frictional and aerodynamic losses
  • The front vehicle would be responsible for overcoming the frontal aerodynamic force and cutting the vehicle through the air.
  • Each module is running an energy surplus which is transmitted to front carriage not by force, but by electricity. With this approach, it doesn’t require structural strength on the part of the carriages to transmit the energy.
  • Spreadsheet of Energy Input / Energy Output

Front Carriage (1 x)

front carriage 1

  • 2.1 m long, 1m wide and 0.5 m wide
  • 15 kw/h of battery capacity
  • 500 w motor, at 41.76 km/h is it outputting 300 w
  • It has a coefficient of drag of 0.18 and a frontal area of 0.6 m^2
    • At 41.76 km/h it requires 220 w to offset aerodynamic forces, plus another 70 w for rolling friction

Cargo Carriage (24 x)

 

 

  • 2.2 m long body, 1 m wide, 0.5 m high
  • At an average of 41.76 km/h, the cargo carriage runs a surplus of 50 w over 24 hours. 100% concentrated in the 10 am to 2 pm time window.
  • Carriage weight 125 kg
  • 2.5 kw/h energy storage
  • Cargo carried 200 kg
  • Rolling Resistance 45 w
  • Aerodynamic resistance at 41.76 km/h is 25 w as it is largely protected from drag by the carriage in front of it

Energy Collection & Storage

  • Solar input per carriage, average of 200 w per 12 hours of daylight. Peak power 340 w
    • This gives a solar budget of 2.4 Kw/h per carriage, for a total power budget of 57.6 kw/h per day.
    • Assuming 35% of the energy is used directly, with no loss. The total budget is reduced to 48.96 kw/h

Energy Breakdown

  • Total Energy budget of 55 kw/h
  • Energy Expenditure on aerodynamic losses
    • Front Carriage  (7 kw/h)
    • Cargo Carriage (1.6 kw/h, times 24 carriages 38.52 kwh)
  • Energy Expenditure on Rolling Friction
    • Front Carriage (1.68 kw/h)
    • Cargo Carriage (1.08 kw/h, times 24 carriages 25.92 kw/h)

Spreadsheet of Energy Input / Energy Output

Guesses/Assumptions

  • The coefficient of drag and rolling resistance are estimates taken from other similar objects
  • The solar radiation captured per day is crudely modelled

Optimisations not used

  • It would make sense move slightly quicker the stronger the sun was shining as energy is wasted during the storage process. (move slightly quicker at midday, slower at night)
  • The gaps between the carriages could be more effectively covered reducing drag further, 50% of the energy lost is the aerodynamic losses from the carriages

Losses not estimated

  • The last carriage will experience extra drag from the turbulence left behind it
  • Loss of efficiency within the electric motor
  • Connection loss transmitting power between 24 carriages.
  • Energy used to turn the wheels, or to correct path
  • Headwinds, cross winds

References

Spreadsheet of Energy Input / Energy Output

Rolling Resistance
Large Battery

Banking Sector Size and Margins per Country

The charts below compare the banking sector in four different countries, which have populations ranging from 6m to 325m people.

The smaller the country, the higher the revenue and margins. Australia’s lack of volatility in banking sector margins is striking. Margins should be mean-reverting in a competitive market. The remarkable stability suggests a lack of competition.

Banking_revenue_per_capitaBanking_profit_per_capitaBanking_revenue_percentage_of_gdpBanking_profit_percentage_of_gdp

Let’s Psychologically Anchor Autos to the Total Cost of Ownership

The automobile is of great prominence in American life. There are 260 million of them on the roads and 85% of people use them to get to work. At 14% of expenditure they are the second biggest expense, after the cost of a home.

These products have improved immensely in quality, comfort and safety over the years. Each one represents a multi-billion dollar investment on behalf of its creator–in design, research and development, and the production line to manufacturer it.

An equally impressive level of investment goes into the promotion and sale of these products. As 85% of vehicles are financed/leased, Automakers place heavy emphasis on monthly finance payments, “Lease from $299/month, Finance for $399 a month for 60 months.” This psychologically anchors customers to a number that doesn’t represent the complete cost of operating the product.

Physiological Anchoring is a powerful cognitive bias, it’s the common human tendency to rely heavily on the first piece of information presented. “$199 a month” becomes embedded as a price, even if the total cost of transport is many times higher than that.

Amortisation of the deposit/down-payment, the cost of insurance, maintenance, fuel and depreciation(assuming it’s not a lease) melt away into a blur of general expenditure. Buyers underestimate their total transport costs. The result could be financial strain, misery and potential default.

The result of this miscalculation is a higher percentage of the customers expenditure going to the automaker.

Progress has been made in limited areas, such as the EPA/DOT disclosure on the annual fuel cost of operating the vehicle.

It’s a start, but it could be so much more.

The cost of operating a vehicle should be an industry standard. The numbers would be consolidated for 1 month and 3 year periods. (3 years corresponds to the warranty period of most vehicles.)

All advertising which quotes a lease rate, finance rate or RRP would be required to first display and quote the TCO, or total cost of ownership per month in equal prominence. This would help nullify the artificially low anchor set by the finance rate. Rather anchoring on the lease rate of $189/month the buyer would hopefully anchor the number presented first, for example $506/month.

Additionally there would be a sticker of A4 size, placed on each vehicle. It would be required that a dealer show the customer this information for any vehicle they are purchasing.

As insurance rates differ significantly by state, for example Michigan $213/month vs Ohio $71/month the TCO could be state specific.

The numbers are an estimate, the depreciation curve for each vehicle is an estimate. It depends on many factors. The point is not that it represents an exact amount the customer will pay, but that it correctly anchors them to the correct ballpark for transportation costs they are about to commit to.

Below are some examples of what it could look like. It would allow for direct comparison for models across different manufacturers. The numbers below are an educated guess for illustration purposes.

Let’s call it the TCO Sticker.