Analyzing Results
Learning Objectives
Students will be able to:
- Graph PM2.5 decay data and identify patterns
- Calculate actual CADR from test results
- Compare their results to theoretical predictions
- Identify design factors that affected performance
Graphing Your Data
Create a line graph showing PM2.5 concentration over time.
Graph Setup
- X-axis: Time (minutes) — 0, 2, 4, 6, 8, 10
- Y-axis: PM2.5 concentration (μg/m³)
- Title: "PM2.5 Decay During CR Box Operation"
- Plot each data point and connect with a smooth curve
What a Good Decay Curve Looks Like:
PM2.5
80 |*
| *
60 | *
| *
40 | * *
| * *
20 | * * *
|______________________________
0 2 4 6 8 10 12 14 16
Time (min)
A well-performing CR box shows:
- Steep initial decline — rapid particle removal at the start
- Gradual leveling off — approaching minimum concentration
- Smooth curve — not erratic jumps
Calculating Actual CADR
CADR Estimation Formula
Where: Room Volume in cubic feet, Before/After are PM2.5 readings, Test Time in minutes, ln = natural logarithm
Example Calculation
- Room: 300 sq ft × 9 ft ceiling = 2,700 cu ft
- Before: 80 μg/m³
- After: 25 μg/m³
- Test time: 10 minutes
Step 1: Before ÷ After = 80 ÷ 25 = 3.2
Step 2: ln(3.2) ≈ 1.16
Step 3: 2,700 × 1.16 = 3,132
Step 4: 3,132 ÷ 10 = 313 CFM
Calculate Your CADR
Step 1: Before ÷ After = ____ ÷ ____ = ____
Step 2: ln(answer) = ln(____) = ____
Step 3: Room Volume × Step 2 = ____ × ____ = ____
Step 4: Step 3 ÷ Test Time = ____ ÷ 10 = ____ CFM
Comparing to Commercial Units
| Air Purifier Type | Typical CADR | Typical Cost |
|---|---|---|
| Budget HEPA purifiers | 100-200 CFM | $100-150 |
| Mid-range HEPA | 200-400 CFM | $200-400 |
| High-end HEPA | 400-600 CFM | $400-800 |
| Our CR boxes | 300-700 CFM | $60-100 |
Key insight: CR boxes often deliver commercial-grade performance at a fraction of the cost!
Why Results May Differ from Predictions
| Factor | Effect on CADR |
|---|---|
| Seal quality | Poor seals = air bypasses filters = lower CADR |
| Fan restriction | Partial blockage = less airflow = lower CADR |
| Filter condition | Dirty/damaged filters = lower efficiency |
| Test conditions | Door opened, movement = interference with results |
| Sensor placement | Too close/far from CR box = inaccurate reading |
Reflection Questions
- What was the biggest factor affecting your CR box's performance?
- If you could rebuild, what would you change?
- What design features should we prioritize in the optimization challenge?
Exit Ticket
- Your CR box reduced PM2.5 from 60 μg/m³ to 20 μg/m³. What is the percent reduction?
- Look at your decay graph. During which 2-minute interval did your CR box remove particles fastest? How do you know from the graph?
- Our calculated CADR values were [higher/lower] than our theoretical predictions. Give ONE reason why this might have happened.