EPA Method 1 Sample & Velocity Traverses

EPA Reference Method

Method 1
Sample & Velocity Traverses

Complete interactive guide for determining the number and location of sampling points in stationary source stacks and ducts — with built-in calculators for every equation.

☰ Table of Contents

1Scope & Applicability 2Principle & Summary 3Circular Duct — Traverse Points 4Log-Linear Rule — Point Locations 5Rectangular Duct — Traverse Points 6Log-Tchebycheff Rule 7Cross-Sectional Area 8Pitot Tube Velocity Equation 9Gas Density Calculation 10Volumetric Flow Rate 11Stack Diameter from Circumference 12Quick Reference Summary

1

Scope & Applicability

EPA Method 1 is titled "Sample and Velocity Traverses for Stationary Sources." It provides the procedure for determining the number of sampling or velocity measurement points and their location across a stack or duct cross-section.

The method applies to all EPA reference methods (Methods 2 through 8 and beyond) that require measuring gas velocity, extracting a gas sample, or both. Every test that uses a pitot tube, a sampling probe, or any other measurement device inserted into a stack depends on Method 1 to define where those measurements must be taken.

Key Point Method 1 does NOT measure anything by itself. It tells you HOW to set up the measurement grid. The actual velocity measurement is done by Method 2, and actual sampling by Methods 3–8.

The method covers two duct geometries:

1. Circular (round) stacks and ducts — uses the log-linear rule to place points along two perpendicular diameters.
2. Rectangular ducts — uses the log-Tchebycheff rule to distribute points across the cross-section grid.

The goal is always the same: ensure the set of measurement points is statistically representative of the entire gas flow so that the final calculated velocity and emission rate are accurate.

Important The sampling site must be selected to avoid cyclonic flow, reverse flow, or highly asymmetric velocity profiles. Method 1 requires the measurement location to be at least 8 stack diameters downstream and 2 stack diameters upstream of any flow disturbance (bend, fan, expansion, contraction). If this is not possible, additional traverse points may be required.

2

Principle & Summary

The velocity profile in a duct is NOT uniform — it is higher near the center and lower near the walls due to friction and boundary layer effects. If you measure velocity at only one point, you get a wrong answer. Method 1 solves this by creating a traverse: a pattern of points that, when averaged, reproduces the true mean velocity.

How it works for circular ducts:

1. Measure the stack inner diameter (D).
2. Determine the minimum number of traverse points from a lookup table based on D.
3. Place points along two diameters at distances specified by the log-linear rule (as fractions of D from the wall).
4. Measure velocity or extract sample at each point.
5. Compute the arithmetic average of all point values.

How it works for rectangular ducts:

1. Measure duct width (W) and height (H) to compute area A = W × H.
2. Determine minimum number of points from a lookup table based on A.
3. Distribute points in a grid using the log-Tchebycheff rule for fractional positions.
4. Measure and average as above.

Why Log-Linear? The log-linear weighting accounts for the shape of the turbulent velocity profile in fully developed pipe flow. It gives more weight to regions where the velocity gradient is steeper (near the wall) and less weight to the relatively flat center region. This produces a more accurate average than equal spacing.

3

Circular Duct — Number of Traverse Points

For a circular stack, the minimum number of traverse points depends on the inside diameter D. The total number of points is always 2 × n, where n is the number of points per diameter. Points are placed on two perpendicular diameters.

Stack Diameter (ft)	Min. Points per Diameter (n)	Total Points (2n)
0.12 – 0.25	3	6
> 0.25 – 0.50	4	8
> 0.50 – 1.0	5	10
> 1.0 – 2.0	6	12
> 2.0 – 4.0	7	14
> 4.0 – 8.0	8	16
> 8.0	9	18

Note If the diameter is measured in inches, convert to feet first: D(ft) = D(in) / 12. If measured in meters, convert: D(ft) = D(m) × 3.28084.

Calculator: Find Number of Traverse Points

Stack Diameter Enter value in inches

Unit Inches Feet Meters Centimeters

Result

4

Log-Linear Rule — Point Locations

Once you know how many points per diameter (n), the log-linear rule gives the fractional distance from the inside wall for each point. These fractions are multiplied by the radius (R = D/2) to get the actual insertion depth from each wall.

The points are arranged symmetrically: if the fractional distance from one wall is p, the corresponding point on the opposite side is at (1 − p) from that wall.

Points per Diameter (n)	Fractional Distances from Wall (pi)
3	0.0594, 0.2500, 0.7500
4	0.0359, 0.1942, 0.6458, 0.8058
5	0.0257, 0.1463, 0.5000, 0.8537, 0.9743
6	0.0200, 0.1175, 0.4063, 0.5937, 0.8825, 0.9800
7	0.0163, 0.0983, 0.3404, 0.5000, 0.6596, 0.9017, 0.9837
8	0.0138, 0.0846, 0.2935, 0.4372, 0.5628, 0.7065, 0.9154, 0.9862
9	0.0119, 0.0746, 0.2590, 0.3866, 0.5000, 0.6134, 0.7410, 0.9254, 0.9881

Insertion Depth from Wall

d_i = p_i × R = p_i × (D / 2)

d_i

= insertion depth from wall for point i

p_i

= fractional distance from wall (from table above)

R

= stack inside radius

D

= stack inside diameter

Calculator: Compute Point Locations (Log-Linear)

Stack Inside Diameter Same unit for all output depths

Points per Diameter (n) 3 points 4 points 5 points 6 points 7 points 8 points 9 points

Point Locations (Depth from Wall)

Interactive cross-section showing traverse point layout

5

Rectangular Duct — Number of Traverse Points

For rectangular ducts, the minimum number of points is based on the cross-sectional area. Points are distributed in a grid pattern.

Duct Area (ft²)	Minimum Total Points
< 4	9
4 – 12	12
> 12 – 25	16
> 25 – 36	20
> 36 – 49	24
> 49 – 64	30
> 64	36

The total points must be arranged in a grid as close to square as possible. For example, 12 points could be arranged as 4 × 3 or 3 × 4.

Calculator: Rectangular Duct Traverse Points

Duct Width Feet

Duct Height Feet

Result

6

Log-Tchebycheff Rule — Rectangular Point Positions

For rectangular ducts, point positions along each axis are determined by the log-Tchebycheff rule. The fractional positions depend on the number of measurement lines along that axis.

Lines per Axis	Fractional Positions from Wall
3	0.136, 0.500, 0.864
4	0.097, 0.394, 0.606, 0.903
5	0.076, 0.321, 0.500, 0.679, 0.924
6	0.063, 0.270, 0.440, 0.560, 0.730, 0.937
7	0.054, 0.235, 0.390, 0.500, 0.610, 0.765, 0.946
8	0.047, 0.209, 0.351, 0.452, 0.548, 0.649, 0.791, 0.953
9	0.042, 0.189, 0.321, 0.413, 0.500, 0.587, 0.679, 0.811, 0.958

Position Along Axis

x_i = t_i × W   |   y_j = t_j × H

t_i, t_j

= fractional positions from log-Tchebycheff table

W

= duct width

H

= duct height

Calculator: Log-Tchebycheff Grid Positions

Duct Width Feet

Duct Height Feet

Lines Along Width 3 4 5 6 7 8 9

Lines Along Height 3 4 5 6 7 8 9

Grid Coordinates (from corner)

7

Cross-Sectional Area Calculation

The cross-sectional area is needed to convert average velocity to volumetric flow rate. It is calculated differently for circular and rectangular ducts.

Circular Duct Area

A = π × (D / 2)² = π × D² / 4

A

= cross-sectional area

D

= inside diameter

π

= 3.14159265

Rectangular Duct Area

A = W × H

W

= duct width

H

= duct height

Calculator: Cross-Sectional Area

Duct Shape Circular Rectangular

Diameter Inches

Width Feet

Height Feet

Cross-Sectional Area

8

Pitot Tube Velocity Equation

The standard (Type S) pitot tube measures the velocity pressure (ΔP), which is the difference between total pressure and static pressure. This is converted to gas velocity using the following equation from EPA Method 2 (which relies on Method 1 for point placement).

Stack Gas Velocity

v_s = K_p × C_p × √(ΔP × T_s / (M_s × P_s))

v_s

= stack gas velocity (ft/s or m/s)

K_p

= pitot tube coefficient (typically 0.84 for standard Type S)

C_p

= 85.49 (for ft/s) or 34.97 (for m/s)

ΔP

= velocity pressure (in. H₂O)

T_s

= absolute stack gas temperature (°R or °K)

M_s

= molecular weight of stack gas (lb/lb-mole)

P_s

= absolute stack gas pressure (atm)

Unit Consistency If using ft/s: T_s in °R = °F + 460, P_s in atm. If using m/s: T_s in °K = °C + 273, P_s in atm. Do NOT mix unit systems.

Calculator: Pitot Tube Velocity

Pitot Coefficient (K_p)

Output Unit ft/s m/s

Velocity Pressure (ΔP) in. H₂O

Stack Gas Temperature °F (for ft/s)

Molecular Weight (M_s) lb/lb-mole

Stack Pressure (P_s) atm

Stack Gas Velocity

9

Gas Density Calculation

The dry gas density is needed for several emission calculations. It can be derived from the ideal gas law using molecular weight, temperature, and pressure.

Dry Gas Density

ρ_d = M_d × P_s / (R × T_s)

ρ_d

= dry gas density (lb/ft³ or kg/m³)

M_d

= dry molecular weight (lb/lb-mole or kg/kg-mole)

P_s

= absolute pressure (atm)

R

= 0.7302 (for lb, ft³, atm, °R) or 0.08206 (for g, L, atm, °K)

T_s

= absolute temperature (°R or °K)

Wet Gas Density

ρ_w = M_s × P_s / (R × T_s)

M_s

= wet molecular weight of stack gas

Calculator: Gas Density

Molecular Weight (M) lb/lb-mole

Pressure (P_s) atm

Temperature °F

Output Unit lb/ft³ kg/m³

Gas Density

10

Volumetric Flow Rate

The volumetric flow rate is the product of the average velocity (determined from Method 1 traverse + Method 2 pitot measurements) and the cross-sectional area.

Volumetric Flow Rate (Actual Conditions)

Q_s = v_s × A × 60

Q_s

= volumetric flow rate (actual cubic feet per minute, ACFM)

v_s

= average stack gas velocity (ft/s)

A

= cross-sectional area (ft²)

60

= conversion from seconds to minutes

Dry Volumetric Flow Rate (Standard Conditions)

Q_sd = Q_s × (1 − B_ws) × (T_std / T_s) × (P_s / P_std)

Q_sd

= dry standard volumetric flow rate (DSCFM)

B_ws

= moisture fraction (from Method 4)

T_std

= 528 °R (68 °F) or 293 °K (20 °C)

P_std

= 1.0 atm

Calculator: Volumetric Flow Rate

Average Velocity (v_s) ft/s

Cross-Sectional Area (A) ft²

Moisture Fraction (B_ws) decimal (0 to 1)

Stack Temp °F

Stack Pressure atm

Volumetric Flow Rate

11

Stack Diameter from Circumference

In the field, it is often easier to measure the stack circumference (by wrapping a tape around the outside) than the diameter directly. The inside diameter must be derived by accounting for the wall thickness.

Inside Diameter from Circumference

D = (C / π) − 2 × t

D

= inside diameter

C

= outside circumference (measured with tape)

π

= 3.14159265

t

= wall thickness

Calculator: Inside Diameter from Circumference

Outside Circumference Inches

Wall Thickness Inches

Output Unit Inches Feet Meters

Inside Diameter

12

Quick Reference Summary

Use this table as a field reference card. All the key decisions and equations in one place.

Task	Method / Rule	Key Input
Circular: Number of points	Diameter lookup table	Inside diameter D
Circular: Point positions	Log-linear rule	n (points/diameter), R = D/2
Rectangular: Number of points	Area lookup table	A = W × H
Rectangular: Point positions	Log-Tchebycheff rule	Grid lines per axis
Inside diameter	D = C/π − 2t	Circumference C, thickness t
Cross-sectional area (circle)	A = πD²/4	Diameter D
Velocity	v = KpCp√(ΔPT/MsPs)	ΔP, Ts, Ms, Ps
Gas density	ρ = MP/(RT)	M, Ps, Ts
Volumetric flow (ACFM)	Q = v × A × 60	v, A
Dry std. flow (DSCFM)	Qsd = Qs(1−Bws)(Tstd/Ts)(Ps/Pstd)	Qs, Bws, Ts, Ps

Field Tip Always verify the inside diameter by measuring at least two perpendicular diameters with a tape or caliper at the sampling location. Never assume the nominal diameter equals the actual inside diameter — corrosion, buildup, and construction tolerances can cause significant errors.

Critical Reminder EPA Method 1 requires at least 8 stack diameters downstream and 2 diameters upstream of any flow disturbance. If this criterion cannot be met, you must either find a different location or add more traverse points and document the deviation. Regulatory agencies may reject data taken at non-compliant sites.

EPA Method 1 Interactive Guide | Based on 40 CFR Part 60, Appendix A

Calculators are for educational and planning purposes. Always refer to the official EPA method text for compliance testing.