Cross Sectional Areas in Ports
Measurement Methods and Calculations© by Harold Bettes
Introduction
It is a common mistake that many engine builders and cylinder head modifiers make when they simply multiply the height of the port times its width. Use of that calculation for area without considering the effect that either an irregular shape or the radii in the corners have on the final answer generates errors in engine program computer simulations, calculations, and evaluations.
The majority of typical ports are somewhat rectangular with various radii used in the corners. This rectangular port configuration is the most common for intake ports while exhaust ports may use the rectangular, square, or variations in most cylinder head applications. Some ports are shaped in a somewhat oval configuration. Some port shapes use the generally rectangular configuration, but have a different radius in each corner and are irregular in shape. Some port configurations might also look a great deal like church windows.
Regardless of the shape of the ports (intake or exhaust), it is possible to measure them and do so accurately. Gaining knowledge of the cross sectional area so that sound decisions concerning port velocity can be used is a reality by application of the methods described in the following sections.
Accurate area measurements of ports, runners, and manifolds are generally very difficult. However, the following methods will assist in making both easy and accurate measurements.
The description of each method of measuring and calculating the port area will also present the conversion to square feet so that it is easy to use with flowbench data which is normally in CFM (cubic feet per minute)
Port Velocity
The mention of port velocity might seem more like a buzz-word to the majority of engine bulders and cylinder head modifiers. The very few that understand and properly apply the knowledge to attain correct and complimentary port velocities are the recipients of some free power and reputations for engines that have superior characteristics (power range - spread from peak torque to peak power).
What is the velocity and how high is too much? A good target velocity in engine operation should be no greater than 55% to 57% of the speed of local sound. This can also be referred to as .55 to .57M. The Mach number references the speed of sound and is named for Ernst Mach (1838-1916). Mach was a physicist, philosopher and early pioneer in studying the speed of sound. The speed of sound is 1087 ft/sec at 32°F with an increase of 1.1 ft/sec/°F.
The calculation for the speed of sound (Vsound) in ft/sec is approximately:
Vsound » 1052 + (1.1 x T), where 1052 = an adjustment constant and T = °F.
At this point, note that when considering the airflow of an engine, there is no difference in manifolding, connecting runners, or ports in the cylinder heads, as they are all an extension of the same flowpath. Also note that the various differences in cross sections (areas) allow different local velocities. If we look carefully at the geometry of the flowpath within the engine, it should become apparent that the smallest area will yield the highest local velocity. Evaluating the airflow path of the engine and averaging the lowest velocity with the highest velocity will allow a consideration of average velocity which truly sets the characteristics of the engine, but it is the minimum cross section that establishes the maximum velocity.
Methods of Area Measurement
The area of a square or a rectangle is width (W) times height (H). In the case of a square, both sides are the same, but using the H x W approach will work. The real problem occurs in the corners where there are radii used to form the port of the manifold, runner, or duct in the flowpath.
Because the calculation for the area of a circle is well known, then it can be applied to calculate the equivalent area of either a rectangular or an irregularly shaped port cross section. Even egg-shaped or church window shaped ports can be accurately measured for cross sectional area with this method.
The measurement of the area would be very easy by using a planimeter, but they are very difficult to find and are very expensive if you do find one.
Port (rectangular) Cross Sections - Method 1
It is always easier to evaluate and analyze a problem if you make a sketch. It also assists you in making sure that all the details are allowed for. To calculate the area of a port with the following dimensions H, W, Rcnr. So, the area is (H) x (W) - Acnr = Aprt; where Acnr = Area of corners, Aprt = Area of port (in2). H = height of port, W = width of port. Rcnr x 2 = Dcnr. Dcnr2 x .7854 = Area of circle for the corner radii. The diameter of the circle scribed using the radius of the corners can be placed in a square of the same dimension, the area of the circle subtracted from the area of the square represents the area of the corners (Acnr).
Example - Where the radius of all four corners is the same: Assume for this exercise that the port measurements for height and width and corner radius is known. Where (H = 2.150", W = 1.060", Rcnr = 1/2") .
Step 1) H x W = 2.279 in2
Step 2) Rcnr x 2 = Dcnr = ½ x 2 = 1
Step 3) Dcnr = 1, so Dcnr2 = 1 x .7854 = .7854in2
Step 4) 1 - .7854 = .2146in2 = Acnr
Step 5) H x W - Acnr = Aprt in2 = 2.279 - .2146 = 2.064in2
Step 6) Aprt / 144 = 2.064 / 144 = .0143ft2
Port Cross Sections - Method 2
The periphery of the cross section can be measured with either a string or stiff wire. By carefully forming the string or stiff wire into all the radii of the corners (even if none are the same) an accurate measurement of that section can be done. Measuring the string or stiff wire provides a length (Cprt). Cprt = pD, where Cprt = Circumference around the port, p= 3.1416, and D = an equivalent diameter. When D is found, D2 x .7854 = Aprt in2. Aprt ft2 = Aprt / 144.
Example - A port with 4 different, but unmeasured, radii in the corners is measured with a stiff wire and the resultant length is measured to be 6.3 inches. What is the area of the port at that location?
Cprt = 6.3, so 6.3 / p = 2.005. D2 x .7854 = (2.005)2 x .7854 = 3.16 in2 = Aprt
Aprt / 144 = Aprt ft2 = 3.16 / 144 = .022ft2
Port Cross Sections - Method 3
This method is sometimes called the "paper doll" method. It uses graph paper cut outs for the different sections to be measured. The preferred graph paper to use is the type that has 10 squares per inch (thus 100 squares per square inch).
The graph paper is cut out so that the graph paper is an image of the port cross section to be evaluated and the squares can be counted. Those squares on the periphery of the cut out that are less than one square are estimated for a value of 1/4, 1/2, or 3/4 of each square for greater accuracy. The total squares are counted and then divide by 100 for the Aprt in square inches. The Aprt / 144 = Asqft.
Example - Graph paper using 100 squares per square inch is used to make a cut out of the port cross section 2" in from the flange surface. The number of little squares counted is 237 (allowing for some around the periphery that were not full squares). What is the area of the port at the location described?
237 / 100 = 2.37in2 = Aprt in2. Aprt / 144 = Aprt ft2 = 2.37/144 = .0165ft2.
Port Cross Sections - Method 4
This method depends upon molds being taken of the port. Various schemes of taking mold impressions have been done for ports, but a favorable process is to use mold maker's rubber (available from several sources). The molds can be sliced into sections at several reference points and then the mold section or "baloney slice" can be placed on graph paper as in Method 3 above and the squares counted and the area is calculated in the same manor.
Port Cross Sections - Method 5
The port can be measured by placing the part (cylinder head, manifold, runner, etc) on a CMM (coordinate measurement machine) unit and the resulting three dimensional "digitizing" of the part can be used to calculate the areas and even volumes and lengths. CMM time is very expensive and measurements from this type approach would be cost prohibitive in normal circumstances.
The use of CNC milling machines for port shaping allows these multiple calculations to be done and supplied with the finished parts. However, this method is not common for normal customers of CNC porting shops because if the shop supplied the data with the cylinder head or manifold, they might be giving away part of their measurement and machining technology as well.
Flowbench Data and Port Area Measurements Provide Local Velocity
As a matter of convenience for this evaluation, SuperFlow flowbenches provide flow data directly in cubic feet of air per minute (CFM). Since we are interested in velocity, it is imperative to know the area of the port. If the port area was expressed in square feet (ft2), then dividing the flow value in CFM by the area in ft2 (square feet) of the port, the result is FPM (feet per minute). Dividing FPM by 60 yields FPS (feet per second). The specific advantage of this method is that it is not invasive (puts nothing in the flowpath) to the port.
Port Velocity Using Flowbench Data and Port Area
Example - Flowbench data = at 25”H2O test pressure of 350 CFM, port area in square feet = .022ft2 (as in Method 2 listed previously) Local velocity at point of area measurement = 350 / .022 = 15909 FPM / 60 = 265.15 ft/sec.
Measurement of Local Velocity with a Pitot Tube
This type of measurement can be done but is fraught with some problems associated with the nature of the Pitot tube itself. The Pitot tube is sensitive to yaw (angle of airstream other than parallel with Pitot tube) relative to the standard direction of the developed flowpath in a port. It is also very difficult to measure the local velocity with a Pitot tube in the vicinity of the "short side radius" (where the flowpath turns from the main stream to the area below the valve). This measurement can be done directly if using a SuperFlow FlowCom with a matching Pitot tube. The indicated local velocity can also be read with a vertical manometer (using the SuperFlow instructions supplied with the Pitot tube).
Measurement of the Effective Flow Area of a Port
This measurement depends upon accurate data from a flowbench and appropriate and complex calculations can be done to establish an effective flow area (EFA, Ae). When the Ae is compared to the physical measurement of the port area in square inches, a correlation can be done to rate the port. The port area is typically measured on a CMM (coordinate measurement machine) with this method. This is another way to rate ports with a Coefficient of Flow (Cf). This methodology is normally used only in the realm of engine designers and engineering personnel assigned to process data for analysis using CFD (computational fluid dynamics).