A Kramer graph is a specific multiple-line 2D geometric symbolic representation of the characteristics of intake, scavenging and exhaust components in a two-stroke cycle engine. They are typically used to visualize the opening time versus area and/ or lift of the following components:
Intake port / valve Scavenging port / valve Exhaust port / valve Reed inlet valve Rotary inlet valve
Description These representations are used to describe corresponding changes in crankshaft angle and port-area. A Kramer graph plots the relation of the open area of various ports with respect to the angle of the crankshaft in a two-stroke engine. So that upon completion of the cycle (one revolution of 360°) there has been no net change in state of the system; i.e. the device returns to the starting position and area which is zero. They do not show the specific configuration of ports like in a port-map, which enables it to illustrate a more useful visualization of port area distribution, This could be useful because different types of port configurations could have the same opening time and area.
Application In these graphs the X-axis represents the crankshaft angle (θ) in degrees, and the Y-axis represents the open area in any square unit of measurement such as mm². To discern the different types of ports each type is given a designated color. For example, (commonly used):
Blue - Intake system Green - Scavenging system Red - Exhaust system Purple - Inlet valve Many engineers and engine tuners prefer to use the version of a polar graph of this concept to compare different engines to one another. These are commonly called "Kramer cams", referring to a four-stroke camshaft.
Origin Kramer graphs are named after Dutch engineer Hans Kramer, who is considered to have been the first to use this type of graph in a publication on the effect of port shape and area on two-stroke cycle engine performance.