Wind Effects on Tall Buildings

Wind Pressure Fundamentals

Wind striking a tall building creates pressure distributions that vary by height, building geometry, and wind direction. These pressures drive air infiltration and exfiltration through the building envelope, affecting HVAC loads, indoor air quality, and occupant comfort.

Wind pressure on building surfaces follows:

$$P_{wind} = 0.00256 \times V^2 \times K_z \times K_{zt} \times K_d \times C_p$$

Where:

• $P_{wind}$ = wind pressure (lbf/ft² or psf)
• $V$ = basic wind speed (mph, 3-second gust)
• $K_z$ = velocity pressure exposure coefficient (height and terrain dependent)
• $K_{zt}$ = topographic factor (terrain features)
• $K_d$ = wind directionality factor
• $C_p$ = external pressure coefficient (surface location and geometry)

For simplified analysis at standard conditions:

$$P_{wind} = 0.00256 \times V^2 \times K_z \times C_p$$

This pressure acts perpendicular to building surfaces, creating positive pressure (pushing inward) on windward faces and negative pressure (pulling outward) on leeward and side faces.

Height-Dependent Pressure Variation

Wind velocity and resulting pressure increase with height above ground. The velocity pressure exposure coefficient $K_z$ quantifies this effect:

$$K_z = 2.01 \times \left(\frac{z}{z_g}\right)^{2/\alpha}$$

Where:

• $z$ = height above ground (ft)
• $z_g$ = gradient height (900-1500 ft depending on terrain exposure)
• $\alpha$ = terrain exposure coefficient (7-11.5 depending on terrain)

For urban terrain (Exposure B) with typical tall building:

Wind pressure at 600 feet exceeds ground-level pressure by 70%. For 90 mph design wind speed:

Ground level (30 ft): $P_{wind} = 0.00256 \times 90^2 \times 0.70 = 14.5$ psf

600 feet: $P_{wind} = 0.00256 \times 90^2 \times 1.19 = 24.7$ psf

This 70% increase in wind pressure dramatically affects infiltration rates at upper floors.

Windward vs. Leeward Pressures

Windward Surfaces

Windward surfaces (facing wind direction) experience positive pressure. Pressure coefficient $C_p$ ranges from +0.6 to +0.8 depending on building geometry.

For flat facade perpendicular to wind, $C_p = +0.8$:

$$P_{windward} = 0.00256 \times 90^2 \times 1.19 \times 0.8 = 19.8 \text{ psf at 600 ft}$$

Positive pressure forces air infiltration through envelope leakage. Curtain wall systems, window perimeters, and construction joints allow air entry under this pressure.

Leeward Surfaces

Leeward surfaces (opposite wind direction) experience negative pressure due to flow separation and wake formation. Pressure coefficient $C_p$ ranges from -0.3 to -0.5.

For leeward facade, $C_p = -0.5$:

$$P_{leeward} = 0.00256 \times 90^2 \times 1.19 \times (-0.5) = -12.4 \text{ psf at 600 ft}$$

Negative pressure pulls air out of building through envelope leakage. Creates exfiltration from interior spaces to exterior.

Pressure Differential Across Building

Total pressure differential from windward to leeward face:

$$\Delta P_{total} = P_{windward} - P_{leeward} = 19.8 - (-12.4) = 32.2 \text{ psf}$$

This 32 psf differential creates significant driving force for cross-building airflow. Without proper compartmentation, wind-driven airflow overwhelms HVAC system control.

Side Surfaces

Side surfaces perpendicular to wind direction experience negative pressures:

• Upstream side corner: $C_p = -0.7$ to -1.0 (highest suction)
• Mid-building side: $C_p = -0.5$ to -0.7
• Downstream side corner: $C_p = -0.3$ to -0.5

Corner regions experience highest negative pressures, creating localized exfiltration and potential comfort problems.

Infiltration and Exfiltration Impacts

Infiltration Load Calculation

Air infiltration through envelope leakage under wind pressure:

$$Q_{infiltration} = C_d \times A_{leakage} \times \sqrt{\frac{2 \times \Delta P}{\rho}}$$

Where:

• $Q_{infiltration}$ = infiltration rate (cfm)
• $C_d$ = discharge coefficient (0.6-0.65 typical)
• $A_{leakage}$ = effective leakage area (ft²)
• $\Delta P$ = pressure differential (lbf/ft²)
• $\rho$ = air density (0.075 lbm/ft³)

Converting to standard form:

$$Q_{infiltration} = 2610 \times C_d \times A_{leakage} \times \sqrt{\Delta P_{psf}}$$

For curtain wall system at 600 feet with:

• Effective leakage area: 0.1 ft² per 100 ft² of wall area
• 10,000 ft² floor area with 50% exterior wall (5,000 ft²)
• Total leakage area: 5 ft²
• Wind pressure differential: 32.2 psf (from earlier calculation)

$$Q_{infiltration} = 2610 \times 0.65 \times 5 \times \sqrt{32.2} = 48,100 \text{ cfm}$$

For 10,000 ft² floor with 9-foot ceilings (90,000 ft³):

• Air change rate: 48,100/90,000 × 60 = 32 ACH
• This exceeds typical HVAC system capacity by factor of 10-20

This demonstrates why wind-driven infiltration dominates HVAC loads on upper floors during high wind events.

Heating and Cooling Load Impacts

Additional HVAC load from infiltration:

Sensible Load: $$q_{sensible} = 1.08 \times Q \times \Delta T$$

Where:

• $q_{sensible}$ = sensible heat load (Btu/hr)
• $Q$ = infiltration rate (cfm)
• $\Delta T$ = indoor-outdoor temperature difference (°F)

For 48,100 cfm infiltration at 70°F indoor, 0°F outdoor:

$$q_{sensible} = 1.08 \times 48,100 \times 70 = 3.64 \text{ million Btu/hr}$$

This equals 303 tons of cooling/heating—for a single 10,000 ft² floor.

Latent Load (summer conditions): $$q_{latent} = 0.68 \times Q \times \Delta W$$

Where:

• $q_{latent}$ = latent heat load (Btu/hr)
• $\Delta W$ = humidity ratio difference (grains/lb)

Summer infiltration also introduces moisture requiring dehumidification capacity.

Envelope Performance Requirements

Managing wind-driven infiltration requires high-performance envelope:

Air Leakage Ratings:

• Standard curtain wall: 0.06 cfm/ft² at 1.57 psf (6.24 psf)
• High-performance curtain wall: 0.06 cfm/ft² at 6.24 psf (better sealing)
• Premium curtain wall: 0.06 cfm/ft² at 12.48 psf

At 32 psf wind pressure, even premium curtain wall experiences significant leakage. Design must account for actual infiltration at design wind conditions.

Pressure Equalization: Modern curtain wall systems use pressure equalization principles:

• Rainscreen principle with equalized cavity behind exterior surface
• Reduces net pressure across air barrier
• Interior seal provides primary air barrier
• Exterior surface sheds water but not primary air seal

Properly designed pressure-equalized systems reduce infiltration by 50-80% compared to single-barrier systems.

Building Sway and Movement

Tall buildings experience lateral displacement (sway) under wind loads. This movement affects HVAC distribution systems.

Displacement Magnitude

Top-of-building lateral displacement:

$$\delta_{max} = \frac{F_{wind} \times H^3}{3 \times E \times I}$$

Where:

• $\delta_{max}$ = maximum lateral displacement (inches)
• $F_{wind}$ = total wind force (lbf)
• $H$ = building height (inches)
• $E$ = modulus of elasticity (psi)
• $I$ = moment of inertia (in⁴)

Typical tall building displacement:

• 40-story (520 ft): 6-12 inches at top
• 60-story (780 ft): 12-24 inches at top
• 80-story (1040 ft): 20-40 inches at top

Buildings designed for maximum displacement of H/400 to H/500 under 10-year wind event.

Inter-Floor Differential Movement

More critical than total displacement: differential movement between floors.

For uniform building: $$\delta_{differential} \approx \frac{\delta_{max}}{n_{floors}}$$

Where $n_{floors}$ = number of floors.

60-story building with 18-inch top displacement:

• Average inter-floor differential: 18/60 = 0.3 inches
• Upper floors experience greater differential than lower floors
• Maximum inter-floor differential at upper floors: 0.4-0.6 inches

Impact on Ductwork and Piping

Building movement requires flexible connections in HVAC distribution:

Ductwork:

• Rigid duct connections fail under cyclic movement
• Flexible connections every 3-5 floors on vertical risers
• Expansion joints accommodate differential movement
• Slack or loops in horizontal duct near vertical penetrations

Piping:

• Rigid pipe systems experience high stress under building movement
• Flexible connectors at floor penetrations
• Expansion loops or flexible hose sections
• Pipe supports allowing movement while preventing excessive stress

Equipment Isolation:

• Equipment mounted rigidly to floor structure moves with building
• Connections to distribution systems must accommodate differential movement
• Vibration isolation must allow lateral movement without damage
• Spring isolators designed for lateral displacement capacity

Design Approaches

Flexible Connections:

• Canvas or rubber fabric connections in ductwork
• Braided flexible hose in piping
• Expansion joints sized for building movement plus thermal expansion
• Installed with adequate slack for expected displacement

Slip Joints:

• Telescoping duct or pipe sections
• Sealed with flexible gaskets
• Allow axial movement without leakage
• Common at vertical riser penetrations

Seismic-Rated Connections:

• Components designed for seismic movement also accommodate wind sway
• Higher capacity than standard flexible connections
• Required in seismic zones regardless of wind sway considerations

Dynamic Wind Effects

Vortex Shedding

Wind flowing past building creates alternating vortices (Kármán vortex street). Vortex frequency:

$$f = \frac{S \times V}{D}$$

Where:

• $f$ = vortex shedding frequency (Hz)
• $S$ = Strouhal number (0.2 for rectangular buildings)
• $V$ = wind velocity (ft/s)
• $D$ = building width perpendicular to wind (ft)

When vortex frequency approaches building natural frequency, resonance amplifies motion. HVAC systems must accommodate resulting vibration and movement.

Buffeting and Turbulence

Atmospheric turbulence and nearby building wake effects create time-varying wind pressures:

• Pressure fluctuations ±20-40% of mean pressure
• Frequency range: 0.1-5 Hz
• Creates cyclic infiltration/exfiltration

HVAC System Response:

• Variable infiltration affects zone pressurization
• Rapid load changes challenge control systems
• Pressure-independent VAV terminals recommended for perimeter zones
• Supply air volume modulates to maintain comfort despite load variations

Galloping and Flutter

Extreme wind conditions can induce building oscillations:

• Galloping: low-frequency, large-amplitude motion
• Flutter: high-frequency, smaller-amplitude motion
• Both create acceleration forces affecting equipment mounting and connections

Equipment anchorage must withstand dynamic loads from building motion. HVAC components designed for seismic loads typically adequate for wind-induced motion.

HVAC Design Strategies

Perimeter Zone Design

Increased Capacity: Size perimeter zone equipment for infiltration loads at design wind conditions. Typical oversizing: 30-50% at upper floors.

Pressure Control: Maintain slight positive pressure in perimeter zones to reduce infiltration. Target: 0.02-0.05 in. w.c. relative to exterior.

Dedicated Perimeter Systems: Separate perimeter HVAC systems from core systems. Perimeter systems designed for high sensible loads and rapid response. Core systems handle occupancy and internal loads.

Curtain Wall Integration

Coordination: HVAC designer coordinates with curtain wall consultant on:

• Infiltration rates at design wind pressures
• Perimeter supply air delivery strategy
• Integration of heating/cooling with curtain wall mullions
• Condensation control on interior curtain wall surfaces

Radiant Systems: Consider radiant ceiling or floor systems for perimeter zones:

• Addresses high conductive and solar loads independent of air system
• Reduces air system size and infiltration impact
• Provides comfort despite curtain wall temperature variation

Distribution System Flexibility

Flexible Connections: Install flexible connections at:

• All vertical riser floor penetrations
• Equipment connections throughout building
• Locations where differential movement anticipated

Seismic Restraint Coordination: Ensure seismic restraints allow building movement while preventing excessive equipment displacement.

Commissioning Verification: Verify flexible connections installed with appropriate slack and movement capacity.

Envelope Commissioning

Air Leakage Testing: Conduct whole-building or floor-by-floor air leakage testing:

• Blower door testing at representative pressures
• Identify and seal major leakage paths
• Verify curtain wall installation quality
• Test before interior finishes installed when remediation easier

Mockup Testing: Test curtain wall mockups at design wind pressures:

• Verify air leakage rates at actual design pressures
• Test water penetration resistance under simultaneous pressure and spray
• Confirm pressure equalization system performance

Wind effects represent a dominant factor in tall building HVAC design. The combination of height-dependent wind pressures, building geometry effects, and envelope performance determines infiltration loads that can exceed calculated heating and cooling loads by factors of 2-5 during design wind events. Proper envelope design, HVAC system sizing, and distribution system flexibility ensure acceptable performance under the extreme conditions unique to tall buildings.