Satellite internet · Session 7 of 8
Designing under constraint
How do you choose between designs when every option costs something measurable?
A clinic two valleys from the nearest road has a video consultation booked for Tuesday. Whether it happens, whether it survives a dropped link, whether the picture holds — all of that was settled by decisions taken years earlier about frequencies, altitudes and how many satellites to launch. Engineering is not what happens on Tuesday. It is the argument about numbers that happened long before, and the quality of that argument is the whole of the result.
By the end
- Write a measurable requirement that names its failure condition, so that meeting it demonstrates something.
- Close a simple link budget using free-space path loss, and identify the worst-case geometry it must survive.
- Quantify at least one shared-sky cost — brightness in magnitudes or decay time against altitude — and weigh it against a benefit without letting either erase the other.
The idea
Engineering starts with a requirement, and a requirement that the baseline already satisfies is not a requirement but a description. A usable one names the quantity, the threshold and the condition: not “good coverage” but “a usable satellite at 10 of 12 sampled steps with one satellite disabled”. The failure condition is the part that makes the test capable of telling you something you did not already know.
The central calculation in radio design is the link budget: every gain and loss between transmitter and receiver, added up in decibels, with enough left over to be decoded. The dominant term is free-space path loss, which grows as the square of distance: FSPL(dB) = 20 log₁₀ d + 20 log₁₀ f + 92.45, with d in km and f in GHz. At 550 km and 12 GHz that is 168.8 dB; at the 1,123 km edge of the footprint it is 175.0 dB. The 6.2 dB difference is the margin a design must carry simply for being at the edge rather than overhead.
Radio spectrum is a shared, finite and legally allocated resource. Two systems radiating in the same band over the same ground interfere, so the ITU sets limits on equivalent power flux density — how much power a constellation may deliver to a patch of ground — specifically to protect existing geostationary users. A design that ignores this is not merely impolite; it is unlicensable, which makes it not a design.
The night sky is shared too, and the cost can be measured. Astronomers use the magnitude scale, in which smaller numbers are brighter and five magnitudes is a factor of exactly 100 in brightness. The unaided eye reaches about magnitude 6 under dark skies; professional recommendations ask that satellites be kept fainter than magnitude 7, invisible to the eye but still bright enough to streak a long exposure. Operators have tried darkening coatings and sun-shades to reach it, with partial success, and the numbers remain contested.
Orbital debris is a cost that compounds. A collision produces thousands of fragments, each of which can cause further collisions — the runaway case is called the Kessler syndrome. Altitude governs how long the problem persists: at 550 km, residual drag re-enters a dead satellite within a few years, while at 1,200 km the same object stays up for centuries. Choosing a low shell is partly a latency decision and partly a decision to let physics clean up after you.
None of these costs cancel each other. The clinic genuinely gains a connection, and astronomers genuinely lose exposures; both statements are true at once. The job is not to find the argument that makes one disappear, but to state each in its own units, name who bears it, and be explicit about what evidence would change your mind.
Gather
Your earlier models, up to eight satellite tokens, test cards, calculator and a notebook.
Build and investigate
- Choose a community and state its need in one sentence: an island school needs reliable lesson streaming; a mountain clinic needs a route that survives one failure; a ship needs continuous handoffs as its usable satellites change.
- Write a measurable target with its failure condition. For example: at least 10 of 12 coverage steps with one satellite disabled, or at least six packets delivered by 20 s with the direct link blocked. Check the baseline does not already pass — if it does, the target is too weak to be worth testing.
- Draw the design with no more than eight satellite tokens. Label terminal, relay, ground station and destination, mark where power comes from, and state the minimum elevation angle you are assuming.
- Run the baseline under the stated failure condition and record the result honestly, including failures. Change exactly one variable, re-run under identical rules, and record again.
- Close a simplified link budget. Compute FSPL at your zenith slant range and at your worst-case edge range, take the difference in decibels, and state the margin the design must carry. If you raised the orbit, recompute it — the loss grows with distance.
- Quantify one shared-sky cost. Either compare magnitude 7 with magnitude 5 using the factor 2.512 per magnitude, or compare decay time at 550 km with 1,200 km. Then name who bears the cost, who receives the benefit, and what evidence would change your recommendation.
Run the numbers
A design decision is only a decision if the alternatives were quantified. Decibels and magnitudes are both logarithmic scales — treat them carefully.
| Relation | Expression | What it means |
|---|---|---|
| Free-space path loss | FSPL(dB) = 20 log₁₀ d + 20 log₁₀ f + 92.45 | d in km, f in GHz |
| Decibel ratio | dB = 10 log₁₀(P₁ / P₂) | power ratio; 3 dB ≈ ×2, 10 dB = ×10 |
| Link margin | margin = received power − required power | must stay positive at the worst geometry |
| Magnitude difference | Δm = −2.5 log₁₀(b₁ / b₂) | 5 magnitudes = exactly ×100 in brightness |
| Coverage fraction | covered steps ÷ total steps | a sampled estimate, not a continuous guarantee |
Core · Grade 7–8
- Compute FSPL at 550 km and at 1,123 km, both at 12 GHz. Take the difference in decibels and convert it to a power ratio using 10^(dB/10). Which geometry must the design survive?
- Magnitude 7 against magnitude 5: two magnitudes apart. Using a factor of 2.512 per magnitude, how many times fainter is the first? Check your answer against the rule that five magnitudes is exactly 100.
- State your target, your baseline result under the failure condition, and your revised result. Calculate the change, and write one claim your evidence supports — in the same units you measured.
Deeper · Grade 9–12
- Derive the constant in the FSPL formula. Path loss is (4πd / λ)²; substitute λ = c / f and convert to decibels with d in km and f in GHz. Show where 92.45 comes from.
- A design doubles its orbital altitude from 550 km to 1,100 km. Calculate the change in zenith FSPL in decibels, the change in one-way propagation delay, and the change in footprint radius using cos(ε + γ) = (R/r) cos ε at ε = 25°. Present all three as a single table and state what the design bought and what it paid.
- Argue the altitude question with numbers on both sides. Higher means fewer satellites for the same coverage; lower means less path loss, less delay and years rather than centuries of post-failure decay. Name the quantity that decides it for your particular community, and the measurement you would need.
Measure and record
Keep a table of design version, test condition (including the failure applied), target, observed result and next change. Record FSPL at both geometries with the margin in decibels. Use actual model measurements — never write down an observation you did not make.
Worked example
A first design covers 12 of 12 sampled steps with all four satellites working — and that result is worthless, because the target was met before any designing happened. Re-run it under the stated failure condition, one satellite disabled, and the same design covers 9 of 12 = 75%, below the 10-step target. Now a change can be judged. Add a fifth satellite, re-run under the identical failure, reach 11 of 12, and you have evidence: the target is met under failure, with one step still uncovered. The supportable claim is “11 of 12 sampled steps with one satellite disabled”. The unsupportable claim is “never disconnects” — twelve samples cannot see between themselves, and the geometry says the gap is real. Meanwhile the link budget moved too: FSPL at 12 GHz is 168.8 dB overhead and 175.0 dB at the 1,123 km edge, so the design carries 6.2 dB of margin purely for geometry.
Pause and explain
Your revised design uses more satellites and improves sampled coverage from 9 to 11 of 12 under failure. Does that make it the better design? Name three quantities your test did not measure, and for each say what it would take to measure it.
Check your reasoning after your attempt
It is better on one measured criterion under one named condition, which is a real but narrow result. Unmeasured quantities include: capacity, since more satellites in view does not mean more bits per second if they share spectrum, and measuring it needs a traffic model; path loss and link margin, which worsen with slant range and need a link budget at the worst geometry; brightness and debris contribution, which scale with the number launched and need photometry and a decay model; and cost per unit of delivered service. The strength of the claim is not the size of the improvement — it is how precisely you can state the conditions under which it holds.
Save in your mission notebook
The community brief; the measurable target with its failure condition; the before-and-after trial table under identical rules; the FSPL calculation at both geometries; one quantified shared-sky cost with who bears it; one bounded claim and one evidence gap.
Parent / teacher notes
Step 2 is where this lesson succeeds or fails. Make learners check that the baseline does not already pass — the version of this lesson where the target is met before any work happens teaches that measurement is theatre. Assess the structure of the argument, not agreement with a policy position: a learner who recommends the higher orbit with good numbers has done better work than one who recommends the lower orbit because it sounds responsible. Grade 7–8 can use the supplied FSPL values and do the magnitude comparison. Grade 9–12 should derive the 92.45 constant and build the full altitude-tradeoff table.
Suggested timing: 10 minutes predict, 15 read and explain, 30 build and investigate, 25 measure and calculate, 10 independent explanation. Adapt the activities rather than rush unfinished reasoning.
Take it further
Compare the satellite link with a terrestrial alternative for the same community — a fibre run or a microwave relay chain. Estimate the cost per kilometre, the terrain obstacles and the time to deploy, then state which evidence you are missing before a recommendation would be honest. Most real infrastructure decisions are lost or won on exactly that missing evidence.