Previous page

Laser equations

Next page

Results

The equations provided here are rough approximations, given for developing an order of magnitude understanding of what the discussed satellite architectures can achieve.

Coverage per satellite

The coverage per satellite is a simple multiplication of the Earth’s circumference (approximately 40,000km), orbits per day (approximately 15 for LEO), days per year (approximately 365), and the average swath width.

For example, with an average swath width of 10m, the coverage per satellite will be approximately 6,000 square kilometres per day, or 2.19 million square kilometres per year.

Income potential per satellite

The income per satellite is assumed to be $1 per hectare ($100 per square kilometre). This is at a significant discount to existing aerial LiDAR offerings, which typically ask for $3 to $10 per hectare.

Following the previous example, at an annual coverage of 2.19 million square kilometres, the satellite has an earning potential of $219 million per year. This earning potential will of course only be met if the satellite operators are able to fully sell out its capacity. Regardless, this is a useful measure to show the earning potential of a satellite.

Payback period

The payback period is a simple calculation to show the effectiveness of investing in a given satellite. It is calculated by dividing the recurring cost of the satellite by the yearly income potential. The faster the payback period, the better the investment.

Following the previous example, say the satellite costs $200 million to build and launch. Dividing by the earning potential of $219 million per year gives a payback period of 0.913 years, or 10.95 months.

Constellation size needed

We assume a global forest area of 5 billion hectares, a bit higher than the 2020 estimate of 4.02 billion hectares, to allow for growth in forest area in the future. To understand the constellation size needed, an easy approximation is:

$$ N_{sats} = \frac{A_{land}}{A_{cov}(1-f_{cloud})} $$

Where:

• $N_{sats}$ is the approximate number of satellites needed for a constellation capable of mapping all of Earth’s forests once per year.
• $A_{land}$ is the land area of Earth’s forests = roughly 5 billion hectares.
• $A_{cov}$ is the annual coverage per satellite.
• $f_{cloud}$ is the fraction of Earth’s surface that is covered in cloud = roughly 0.7.

Following the previous example, at an annual coverage of 2.19 million square kilometres, we would need a constellation of 76 satellites to map all of Earth’s forests once per year.