Roots Blower Shaft Power

Roots blower shaft power is the mechanical power required at the blower shaft to deliver the required flow at the required pressure. It is the basis for motor sizing. Shaft power is calculated from flow, pressure, and efficiency: BHP = (ACFM × psig) / (229 × ηmechanical). For a 100 HP blower at 8 psig, shaft power is typically 70–80 BHP. Motor size must include a 15–20% safety factor.

Based on field data, shaft power is the single most important factor in motor sizing and energy cost. A 2% efficiency difference on 100 HP continuous duty costs $2,400–3,000 per year. This guide covers shaft power calculation, efficiency factors, motor sizing, and field verification.

Table of Contents

• What Is Roots Blower Shaft Power?

• Shaft Power Formula

• Efficiency Factors

• Motor Sizing

• Pressure vs Power Relationship

• Speed vs Power Relationship

• Field Verification

• Common Mistakes

• Frequently Asked Questions

• Final Thoughts

What Is Roots Blower Shaft Power?

Roots blower shaft power is the mechanical power required at the blower shaft to move the specified flow at the specified pressure. It is measured in brake horsepower (BHP). Shaft power is what the motor must deliver to the blower – after accounting for mechanical losses in the blower.

Key concepts:

• Shaft power = power at the blower shaft

• BHP = Brake Horsepower

• Motor power = BHP × safety factor

• Shaft power excludes motor losses

Based on field data, shaft power is the starting point for motor sizing and energy cost analysis. Accurate shaft power calculation prevents motor overload and energy waste.

Shaft Power Formula

Basic formula:
BHP = (ACFM × psig) / (229 × ηmechanical)

Where:

• BHP = brake horsepower (shaft power)

• ACFM = actual flow at operating conditions

• psig = discharge pressure (gauge)

• 229 = conversion constant

• ηmechanical = mechanical efficiency (0.85–0.92)

Expanded formula (including motor):
Motor HP = BHP × 1.15–1.20 (safety factor)

Example calculation:

• Flow: 500 ACFM

• Pressure: 8 psig

• Mechanical efficiency: 0.89

• BHP = (500 × 8) / (229 × 0.89) = 4,000 / (229 × 0.89) = 4,000 / 203.8 = 19.6 BHP

• Motor HP = 19.6 × 1.15 = 22.5 → 25 HP motor

Quick estimation:
At 8 psig: approximately 18–20 HP per 100 ACFM.
500 ACFM at 8 psig: 90–100 BHP.

Efficiency Factors

Mechanical efficiency (ηmechanical):

• Accounts for losses in bearings, gears, and friction

• Typical: 0.85–0.92

Motor efficiency (ηmotor):

• Accounts for electrical losses in motor

• IE2: 0.91–0.93

• IE3: 0.93–0.95

• IE4: 0.95–0.97

Overall efficiency:
ηoverall = ηmechanical × ηmotor
Typical: 0.88 × 0.94 = 0.827 (82.7%)

Efficiency example:

Motor Sizing

Motor sizing steps:

Step 1 – Calculate BHP.
BHP = (ACFM × psig) / (229 × ηmechanical)

Step 2 – Add safety factor.
Motor HP = BHP × 1.15–1.20

Step 3 – Select standard motor.
Round up to next standard size.

Example:

Safety factor reasons:

• Pressure spikes

• Start-up conditions

• Voltage variations

• Altitude derating

• Future expansion

Altitude derating:

• Motor capacity decreases at altitude

• Derate 1% per 1,000 ft above 3,300 ft

• Motor HP at altitude = motor HP / (1 – derate)

Pressure vs Power Relationship

Power is proportional to pressure:
For constant flow, power ∝ pressure.

Example:

• 500 ACFM at 5 psig: 12.3 BHP

• 500 ACFM at 10 psig: 24.6 BHP

• 500 ACFM at 15 psig: 37.0 BHP

Pressure effect on power:

• Doubling pressure doubles power

• 2 psig increase = 20% power increase

• Higher pressure = higher operating cost

Speed vs Power Relationship

Power is proportional to speed cubed:
For constant pressure, power ∝ RPM³.

Why the cubic relationship:

• Flow ∝ speed

• Power = flow × pressure

• Pressure is constant (system)

• Power ∝ speed × constant × speed²? Actually power ∝ speed³

Energy savings example:

• 80% speed = 80% flow = 51% power

• 60% speed = 60% flow = 22% power

• VFD savings: 25–35% typical

Field Verification

How to verify shaft power in the field:

1. Measure motor amps.

• Measure current at motor terminals

• Record voltage and power factor

2. Calculate input power.
kW = (V × I × √3 × PF) / 1000

3. Calculate shaft power.
BHP = kW × 1000 / 746 × ηmotor

4. Compare to calculated value.

• Within 5%: normal

• 5–10% high: investigate

• 10% high: problem

Verification example:

Check against calculated BHP:

• Calculated BHP: 36.0 HP

• Measured BHP: 38.4 HP

• Difference: 6.7% – investigate

Common Mistakes

1. Using SCFM instead of ACFM.
SCFM undersizes shaft power. Use ACFM at operating conditions.

2. No altitude correction.
At altitude, motor derating required. Derate motor 1% per 1,000 ft.

3. No safety factor.
Undersized motor trips on overload. Use 15–20% safety factor.

4. Wrong efficiency.
Using mechanical efficiency incorrectly. Use manufacturer efficiency data.

5. Ignoring motor efficiency.
Shaft power is BHP – motor power must account for motor efficiency.

6. Pressure at point of use.
Use pressure at blower discharge flange. Pipe losses add 1–3 psig.

7. Oversizing motor.
Oversized motor wastes energy and capital. Use correct sizing.

Frequently Asked Questions

1. What is roots blower shaft power?
Shaft power is the mechanical power required at the blower shaft – measured in brake horsepower (BHP). It is calculated from flow, pressure, and mechanical efficiency. Motor size must be larger due to safety factor.

2. How is shaft power calculated?
BHP = (ACFM × psig) / (229 × ηmechanical). Example: 500 ACFM at 8 psig, ηmechanical = 0.89 → 19.6 BHP.

3. What is the difference between BHP and motor HP?
BHP is power at the blower shaft. Motor HP is the motor size. Motor HP = BHP × safety factor (1.15–1.20). BHP excludes motor losses – motor HP must account for them.

4. What is mechanical efficiency?
Mechanical efficiency accounts for losses in bearings, gears, and friction. Typical: 0.85–0.92. 3-lobe: 0.88–0.92. 2-lobe: 0.82–0.88. Use manufacturer data.

5. What safety factor should I use?
15–20% safety factor. 15% for steady pressure. 20% for variable pressure (aeration, conveying). Never use less than 10%.

6. How does pressure affect shaft power?
Power ∝ pressure (for constant flow). Doubling pressure doubles power. At 15 psig, power is 3× 5 psig. Higher pressure = higher power.

7. How does speed affect shaft power?
Power ∝ speed³ (at constant pressure). At 80% speed, power is 51% of full. At 60% speed, power is 22% of full. VFD saves energy.

8. How do I size a motor?
Calculate BHP. Add 15–20% safety factor. Round up to next standard motor size. Example: 19.6 BHP × 1.15 = 22.5 HP → 25 HP motor.

9. How does altitude affect motor sizing?
Motor capacity decreases at altitude. Derate 1% per 1,000 ft above 3,300 ft. Motor HP at altitude = motor HP / (1 – derate).

10. What is the rule of thumb for motor sizing?
At 8 psig: 18–20 HP per 100 ACFM. 500 ACFM at 8 psig → 90–100 BHP. Add safety factor → 105–120 HP → 125 HP motor.

11. How do I verify shaft power in the field?
Measure motor amps, voltage, power factor. Calculate input power (kW). Calculate shaft power: BHP = kW × 1000 / 746 × ηmotor. Compare to calculated BHP.

12. What is the effect of motor efficiency on shaft power?
Shaft power is BHP – motor efficiency affects electrical input. For 100 HP shaft power, IE2 (92%) input = 100/0.92 × 0.746 = 81.1 kW. IE3 (94%) input = 79.4 kW. IE3 saves 1.7 kW.

13. What is the difference between pressure and vacuum power?
Vacuum power formula: BHP = (ACFM × inches Hg × 0.491) / (229 × ηmechanical). Vacuum power is lower than pressure for same flow. Example: 10 inches Hg vacuum ≈ 5 psig equivalent.

14. Why does shaft power increase with pressure?
Power = flow × pressure / efficiency. Flow is constant – power increases linearly with pressure. Higher pressure = more work = more power.

15. How do I reduce shaft power?
Reduce pressure (if possible). Improve efficiency (maintain clearance, clean filters). Use VFD for variable flow. Use higher efficiency motor. Reduce flow (if possible).

Final Thoughts

After decades of roots blower shaft power analysis, here is my practical advice:

Shaft power drives motor selection and energy cost. BHP = (ACFM × psig) / (229 × ηmechanical). Accurate calculation prevents motor overload and energy waste. Zhanggu and other manufacturers provide efficiency data.

Add safety factor. 15–20% safety factor. Pressure spikes, start-up, and altitude require margin. Undersized motors trip. Oversized motors waste energy. 15–20% is the sweet spot.

Efficiency matters. A 2% efficiency difference on 100 HP continuous duty costs $2,400–3,000 per year. Use correct mechanical efficiency. Use IE3/IE4 motors. Maintain clearance for efficiency.

The bottom line. Roots blower shaft power is the foundation of motor sizing and energy cost. Zhanggu and other manufacturers provide shaft power data. Calculate accurately. Add safety factor. Verify in the field. The investment in correct sizing pays back through reliable operation.