Math Bridge: Why can 87 seconds consume 102 equivalent seconds?

← Back to CoRAD Drone Flight Planning
Math BridgeEmerging ParadigmsStruggle-friendly runway

Why can 87 seconds consume 102 equivalent seconds?

Connect flight time, hover time, current ratio, reserve use, storage loss, and pack sag for the chapter’s drone mission.

Motion Marley, the guideMotion Marley guides
The one targetReplace a time-additive mission check with a current-weighted one.
The chapter case37 s cruise, 50 s hover, 1800 s reference, hover ratio 1.3.
What it buys youA reserve check that exposes hover-heavy missions.

A field team faces an unresolved physical question: Why can 87 seconds consume 102 equivalent seconds? They must answer it before changing hover ratio on the real device. Predict the direction first.

See the relationship before changing it

The figure reads from left to right. The blue card is hover ratio. The middle card applies this page's relationship. The green card is time-only use. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.

Hover ratio changes time-only use An input card leads through the page relationship to the time-only use result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. Hover seconds count more because the model assigns them more current. More stops therefore consume reserve faster than raw mission time suggests.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for hover ratio is 1.3.

  2. 2

    Name the relationship. time-only=4.83%; teq=tflight+ρthover; used=100teq/Tbattery ρ=1.3: teq=102 s; used=5.67%; uplift=17.24%; pack sag=0.900 V

  3. 3

    Substitute the chapter fixture. Set hover ratio to 1.3. The page ledger gives time-only use as 4.83%.

  4. 4

    Read the result. Keep % beside the value. Use it only inside the technical boundary on this page.

Predict, then change hover ratio

Try Predict the direction of time-only use. Move one control, calculate, then check your prediction.

1.3
Chapter baseline
Time-only use

Observe Hover seconds count more because the model assigns them more current. More stops therefore consume reserve faster than raw mission time suggests. Reset the control to 1.3 and compare time-only use.

Explain Only hover ratio moves here. The other chapter fixtures remain fixed.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only hover ratio moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only hover ratio. It replays the chapter fixture; it is not a field prediction.

1. Start with the physical question

Replace a time-additive mission check with a current-weighted one. A reserve check that exposes hover-heavy missions.

Motion Marley: Keep the units and the model boundary visible from the first line.

2. Name every algebra move

1

Keep flight and hover separateDo not add unlike current states yet.

2

Choose a reference currentLet cruise current be 1 unit.

3

Weight hover timeMultiply hover seconds by ρ=Ihover/Icruise.

4

Add equivalent secondsteq=tflight+ρthover.

5

Compare with the reference budgetused=100teq/Tbattery.

3. Reproduce the chapter case

time-only=4.83%; teq=tflight+ρthover; used=100teq/Tbattery
ρ=1.3: teq=102 s; used=5.67%; uplift=17.24%; pack sag=0.900 V

The arithmetic reproduces the chapter case while keeping its assumptions explicit.

4. Try the controlling input

TryMove the control and watch every displayed result come from the shown formula.

Hover ratio
Time-only use
Equivalent seconds
Weighted use
Estimate uplift
Stored charge left
Pack sag
Loaded voltage

ObserveAt 1.30× hover current, the mission becomes 102.00 equivalent seconds and uses 5.67%, rather than the time-only 4.83%.

ExplainHover seconds count more because the model assigns them more current. More stops therefore consume reserve faster than raw mission time suggests.

Technical boundaries.

This compact engine isolates one relationship; it is not a deployment certificate.

Airframe
The 1.3 ratio is illustrative and changes with mass, speed, wind, and propellers
Battery
The 1800 s reference is not a complete discharge curve
Mission
Climb, acceleration, payload, reserve policy, and weather are omitted

Measure the real system and reopen the decision when its inputs change.

5. Measure the mission states

Log current during takeoff, cruise, hover, climb, descent, payload work, and landing. Integrate those samples and preserve the operational reserve.

6. Keep the flight-energy record

Record route, distances, speed, stop count, state times, state currents, payload, wind, temperature, pack health, reserve, result, owner, and retest trigger.

7. Check yourself

Why is the naive result 4.83%?
Answer: (37+50)/1800×100=4.83%.
Why are there 102 equivalent seconds?
Answer: 37 cruise seconds plus 1.3×50 hover seconds equals 102.
Does 5.67% prove the mission is safe?
Answer: No. It is a two-state teaching ledger; measured full-flight energy and the operational reserve govern acceptance.
Honesty boundary.

The worked values are traceable chapter examples or explicitly labelled teaching assumptions.

37 s and 50 s
Explicit chapter mission times
1.3×
Catalog-typical teaching ratio
5.67%
Two-state energy estimate

Correct, not complete: field evidence still decides acceptance.

Return to CoRAD Drone Flight Planning with the maths unpacked →