Sleep Resilience Math: 18 flashcards
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1. What is the formula for sleep debt?
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Sleep debt = (recommended sleep hours) - (actual sleep hours) per night, accumulated over days.
2. If you need 8 hours of sleep but get 6 hours for 5 nights, what is your total sleep debt?
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Sleep debt = (8 - 6) × 5 = 10 hours.
3. Define sleep efficiency and give the formula.
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Sleep efficiency = (total sleep time / total time in bed) × 100%.
4. A person spends 8 hours in bed but sleeps only 6.5 hours. What is their sleep efficiency?
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Sleep efficiency = (6.5 / 8) × 100% = 81.25%.
5. What is the 'recovery sleep' rule of thumb?
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To recover from sleep debt, you need about 1 extra hour of sleep for every 2 hours of debt, spread over several nights.
6. If you have a sleep debt of 10 hours, how many extra hours of sleep do you need to recover?
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About 5 extra hours (10 / 2 = 5), typically distributed over 2-3 nights.
7. What is the 'sleep onset latency' and how is it used in resilience assessment?
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Sleep onset latency is the time it takes to fall asleep. In resilience, shorter latency often indicates better sleep quality and recovery capacity.
8. Calculate sleep onset latency: lights out at 10:30 PM, sleep at 10:45 PM.
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Latency = 10:45 - 10:30 = 15 minutes.
9. What is the 'sleep recovery index' (SRI) formula?
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SRI = (total sleep time on recovery night / total sleep time on baseline night) × 100%.
10. If baseline sleep is 7 hours and recovery sleep is 8.5 hours, what is the SRI?
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SRI = (8.5 / 7) × 100% ≈ 121.4%.
11. What is the 'sleep debt repayment rate' and how is it calculated?
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Sleep debt repayment rate = (extra sleep hours per night) / (total sleep debt) × 100%.
12. If you have a 10-hour sleep debt and you get 1 extra hour of sleep each night, what is your repayment rate per night?
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Repayment rate = (1 / 10) × 100% = 10% per night.
13. What is the 'sleep resilience threshold'?
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The sleep resilience threshold is the minimum sleep duration needed to maintain cognitive and physical performance, often around 7 hours for adults.
14. If your sleep resilience threshold is 7 hours and you sleep 6.5 hours, what is your deficit relative to threshold?
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Deficit = 7 - 6.5 = 0.5 hours (30 minutes).
15. What is the 'sleep recovery curve' and how is it modeled mathematically?
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The sleep recovery curve is a graph of sleep debt reduction over time, often modeled as an exponential decay: $D(t) = D_0 \cdot e^{-kt}$, where $D_0$ is initial debt and $k$ is recovery rate.
16. If initial sleep debt is 10 hours and recovery rate $k = 0.2$ per night, what is the debt after 3 nights?
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$D(3) = 10 \cdot e^{-0.2 \cdot 3} = 10 \cdot e^{-0.6} \approx 5.49$ hours.
17. What is the 'sleep resilience score' and how is it computed?
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Sleep resilience score = (sleep efficiency × 0.4) + (SRI × 0.3) + (100 - (sleep debt in hours × 2)) × 0.3.
18. Calculate sleep resilience score if sleep efficiency = 85%, SRI = 110%, and sleep debt = 4 hours.
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Score = (85 × 0.4) + (110 × 0.3) + (100 - (4 × 2)) × 0.3 = 34 + 33 + (92 × 0.3) = 34 + 33 + 27.6 = 94.6.
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