Tree farm assumptions:

  1. 250,000 square meters (m2) tree farm
  2. A 1 ton tree contains 1 MWh of energy
  3. Each tree takes 10 m2 of space
  4. Total energy for this farm is thus 25 GWh

Wind farm assumptions:

  1. 5 MW turbine
  2. Requires 250,000 m2 of space
  3. Produces 1 GWh per year

Thus it appears trees far more productive than wind turbines. Is this true? Are these assumptions correct?

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    It will probably take more than 25 years to grow a one ton tree. Have you considered how many turbines you could get in a 250k m2 land base? – Derek Andrews Apr 22 '18 at 20:23
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    Trees and turbines generate energies in different condition. Difficult to compare if they first have to be converted. Conversion of energy involves always loss of energy. In addition time scale must be equivalent. If wood as energy product from trees is included all the years of growth must be considered as well. – Salt Apr 22 '18 at 21:21
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    What are your sources for these numbers? Also, are you saying that trees growing in the same space as a given number of wind turbines produce more power... when burned? And what about the time to grow the trees? – LShaver Apr 23 '18 at 2:00
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    I suspect this question has been asked to promote a commercial tree-selling company, but since it's an interesting question I'll leave it open. – THelper Apr 24 '18 at 7:01

Wind turbines do not turn the ground between them into desert. There is still farming and growth of various plants (even trees) possible. It should not be excluded in those comparisons and calculations.

A wind turbine with 3MW power, rotor diameter of 100 meters rotating at a hub hight of 100 meters may allow growing plants with a height up to 25 meters (~ 80 ft).

  • and indeed, plants can be taller, with taller towers. – EnergyNumbers Apr 24 '18 at 7:30
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    Wouldn't tress create turbulence and reduce the efficiency of the towers though? Wind farms typically have only low growing plants such as grass for grazing or grain below them from what I've seen. – Turksarama Sep 4 '18 at 3:43

A tree farm of that size in a temperate climate would only produce ~1.7GWh/y (net). You are overestimating the productive value of trees by a factor of ~15.

A 5MW wind turbine can produce a maximum of ~44GWh a year. Your assumed figure of 1GWh is only 2.3% of its rated capacity. No-one would bother financing/building a turbine on that site if they could only harness 2.3% of the maximum energy possible. The average load factor of on-shore wind turbines in Denmark over a 20-year period was ~21%, so based on those, you are underestimating the productive value of wind turbines by a factor of ~9.

So, having assumed that trees are 15x more productive than they are in the real-world, and having assumed that wind turbines are 9x less productive than they are in the real world, it is clear that your assumptions are wildly incorrect and thus so is your conclusion/suggestion that trees are (or may be) 25x more productive than wind turbines.

The question posed in the title itself is interesting — if a bit vague — so I'll refine the question a bit and present an answer to that based on some real-world numbers and more credible assumptions...

"Under what conditions are trees more productive than wind turbines?"

Deciduous temperate forests have a net primary productivity of ~0.0186 kWh/m²/day. That translates to ~0.775W/m². (Refer to postscript for source and explanation.)

If we use a forest as a guide, a 250,000m² tree farm could thus produce ~193,750W.

250,000m² is a circle 282m in radius.

Turbines need to be separated by 3-10x their sweep diameters for a variety of reasons (flow interference being the main one). Given that site details are unknown, let's use the average of 6.5x.

A 282m radius field could thus support a single turbine with a sweep diameter of (282*2/6.5=) 86m. Such a diameter sweeps an area of ~5800m².

The turbine power output equation — P = 0.5 × ρ × A × Cp × V³ × Ng × Nb — is then rearranged to calculate the wind-speed required to hit the power target.

Assuming 95% gearbox bearing efficiency, 80% generator efficiency, Betz Limit coefficient of performance (0.56), and sea-level air density, the average wind-speed required to generate 193,750W from a 5800m² sweep area is 5.1ms⁻¹ (~18kmh⁻¹). This is the best-case scenario.

Using a more realistic generator efficiency (65%) and coefficient of performance (0.35) means that an average wind-speed of 6.4ms⁻¹ (~23kmh⁻¹) is required.

So, in short, assuming your climate is temperate, and your site is 'average':

  • Trees would be more productive on sites with average wind speed < 6.4ms⁻¹
  • Wind turbines would be more productive on sites with average wind speed ≥ 6.4ms⁻¹

Note: A 6.4ms⁻¹ average wind-speed is quite windy and only occurs in a limited number of places: Global Mean Wind Speed

PS: You can look up the Mean NPP of various ecosystems here. Convert from grams to Joules by multiplying by ~20,000 (for deciduous hardwoods). Then divide by 31,556,952 to convert J/yr to Watts. Example: Temperate Deciduous Forests have a NPP of 1200g/m²/yr. 1200 * 20000 / 31556952 = 0.76W/m². It's possible to get more accurate numbers if you know the mix of species and the latitude, or if you have access to journals behind paywalls, but for general use you can just use the Wikipedia numbers for a satisfactory approximation.

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    Can you provide some of the sources for your values and calculations? It's unclear what you mean by "generator efficiency" when discussing wind turbines, and whether you're comparing the electric energy produced by wind turbines, to what could be produced by combustion of trees. – LShaver Apr 23 '18 at 14:14
  • lmgtfy.com/?q=net+primary+productivity ... lmgtfy.com/?q=generator+efficiency ... lmgtfy.com/?q=wind+turbine+power+equations ... Production of biomass is different to utilisation of biomass. The latter seems irrelevant to the question — so whether it's burnt for heat, consumed as feed, or made into timbers doesn't really matter. Indeed, worrying about utilisation is a distraction that complicates and paralyses analysis. The utility of land is distinct from and different to its productivity. I just calculated the latter because that's all the OP asked for. – Tim Apr 23 '18 at 15:50
  • Power formula added to answer. – Tim Apr 23 '18 at 16:20
  • NPP source and conversion method added to answer. – Tim Apr 23 '18 at 17:19
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    Good approach, but there are some problems. Firstly, generated power is not proportional to wind speed: therefore, taking average windspeed is not a good way to calculate average power. Secondly, there are already stats out there on wind generation from actual windfarms. Thirdly, and this is a problem with the question too, turbines and trees are not mutually exclusive, rarely compete for land, and generate different types of energy. – EnergyNumbers Apr 24 '18 at 7:32

The question assumes a false dichotomy: Trees or turbines. The actual turbine footprint is small, leaving most of the land available for other purposes.

250,000 m2 is roughly 500m x 500m A 100m diameter rotor needs to be more than 500m away from the next one, probably around twice that. This article: https://www.sciencedaily.com/releases/2011/01/110120111332.htm suggests 15 rotor diameters. This favours the argument for trees.

In rolling country, siting turbines on ridges and using valleys for some other function makes sense.

If the tradeoff is to grow biomass for fuel use, you have a whole bunch of other considerations. The bugbears of biomass use for fuel in temperate climates are harvest, transport, and seasonal storage. Efficiency of the biomass to electricity is a problem too.

The uses don't have to be exclusive: One prominent biofuel candidate is switch grass. Because it doesn't get tree tall, it can be grown right up to the tower right of way. It also has advantages that many farmers already have the equipment to harvest and package (bale) it.

If the terrain is rougher, then space between turbines can be used for pasture.

  • Good points here. Ridges tend to be less productive for biomass production anyway and harvesting is more expensive there. – Jean-Paul Calderone Sep 4 '18 at 12:02

Poplar trees grow quickly. Some commercial sources on the Internet claim that hybrid poplar trees can grow up to 8 ft. per year.

Wind turbines require lots of space:

Draft PPS 18: Renewable Energy. Annex 1 Wind Energy: Spacing of Turbines. A16. Wind turbines need to be positioned so that the distances between them are between 3-10 rotor diameters (about 180-600 metres for a wind farm using 60m diameter, 1.3MW wind turbines) depending on the individual circumstances of the site

Your calculations are actually conservative.

  • This doesn't seem to answer the question. – EnergyNumbers Apr 24 '18 at 7:30

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