Foundations — Requirements — SMART (Specific, Measurable, Achievable, Relevant, Testable)

Before you can judge whether a requirement is "Specific" or "Measurable", you have to be fluent in the tiny alphabet of symbols the parent note quietly uses. This page builds each one from nothing. Read it top to bottom — every symbol is earned before it is used.

1. The comparison operators: $<$, $\le$, $\ge$, $=$

The picture. Imagine a number line — a ruler stretching left (small) to right (big). A requirement paints a region on that ruler where the real spacecraft is allowed to land.

Why the topic needs this. The parent note writes "mass $\le 150$ kg". That is not a wish — it is a line drawn on the ruler. Any built satellite whose mass falls in the green region (left of the line) passes; anything to the right fails. Falsifiability lives entirely in this picture: a requirement is good precisely when it draws a clear line so you can point and say "we are on the pass side."

2. Units, and why a bare number is meaningless

First, the three base units everything else is built from:

Every other unit in this chapter is just these three multiplied and divided together — this is why a number needs a unit to mean anything.

The picture. "$150$" alone could be 150 grams (a phone) or 150 tonnes (a truck). Only the unit fixes which tick-marks on the ruler we are counting.

(Note: the little raised numbers like ${\text{s}}^{-2}$ are exponents — the "how many times multiplied" notation defined in Section 5 below. ${\text{s}}^{-2}$ just means "divided by seconds twice".)

Why the topic needs this. The M in SMART — Measurable — is literally "the requirement carries a unit." Without units, "generate $\ge 2.5$" is not falsifiable: 2.5 what? Watts, kilowatts, horsepower? See Mass Budget and Interface Control Document (ICD), where every line is a number-plus-unit for exactly this reason.

3. Tolerance: $\pm$ and $\%$

The picture. No factory builds anything exactly. So instead of a razor-thin line, tolerance draws a band on the ruler.

Why the topic needs this. Real hardware degrades and varies. A requirement without a tolerance secretly demands perfection, which no test can ever pass. Tolerance is what makes a measurable requirement achievable and testable at the same time.

4. The statistical symbol $\sigma$ (and "$3\sigma$")

The Gaussian assumption. The "$68\%$ / $99.7\%$" rules are not universal — they hold when the scatter follows the bell-shaped normal (Gaussian) distribution, which measurement noise very often does. Under that specific curve, the fraction of measurements landing within $\pm k\sigma$ of the mean is a fixed number:

These percentages are just the area under the bell curve between those limits — the picture makes this concrete.

Why the topic needs this. The parent's traceability example demands altitude knowledge "to $\pm 5$ m $(3\sigma )$." Attaching $3\sigma$ (under the Gaussian assumption) turns a vague "accurate" into a statistical promise: fail no more than about 3 times in 1000. That is what makes an accuracy requirement genuinely testable — see Verification and Validation.

5. Exponents, the natural logarithm $\ln$, and Euler's number $e$

First the notation the rocket equation is written in — exponentiation.

The parent's Achievable example leans on the Tsiolkovsky Rocket Equation, which raises a special base to a power. Build it from zero.

The picture. $e^x$ is a curve that rockets upward ever faster. $\ln (x)$ is that same curve reflected across the diagonal line — it climbs steeply at first, then crawls, and it only exists to the right of $x=0$. They are mirror images because each undoes the other.

Why THIS tool, not simple division? The velocity a rocket gains does not grow in proportion to how much fuel you add — each extra kilo of fuel also has to be carried and accelerated. That "diminishing return" is exactly what $\ln$ captures. In the rocket equation,

$\Delta v=I_{sp}{g}_0\ln \left(\frac{m_0}{m_f}\right)$

doubling your $\Delta v$ needs the mass ratio $m_0/m_f$ to be squared, not doubled — the brutal maths that makes "$\Delta v=50$ km/s on chemistry" absurd.

6. TRL — Technology Readiness Level

The picture. Think of a staircase from "napkin sketch" (bottom) to "flight-proven" (top). The parent's Achievable test — "is it at least TRL 6?" — is asking whether the technology has climbed high enough to be trusted on a real mission. Full ladder: Technology Readiness Levels (TRL).

Prerequisite map

The diagram below shows how each foundation feeds the next. Read it as a flow: comparison operators and base units (top) are the raw grammar; tolerance and $\sigma$ (built from units) make a stated number honest; exponents/$\ln$ together with TRL feed the Achievable check; and all of it converges on a single SMART requirement, which then flows into verification.

In words, the chain reads: operators + units make a number mean something → tolerance and $\sigma$ make that number honest → exponents, $\ln$ and TRL let you check it is possible → together they make the requirement testable.

Equipment checklist

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