# Kramer graph

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> Source: https://en.wikipedia.org/wiki/Kramer_graph
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A **Kramer graph** is a specific multiple-line [2D geometric](/source/2D_geometric_model) symbolic [representation](/source/Depiction) of the characteristics of intake, scavenging and exhaust components in a [two-stroke cycle engine](/source/Two-stroke_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](/source/Reed_valve)
- [Rotary inlet valve](/source/Two-stroke_engine#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](/source/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](/source/X-axis) represents the crankshaft angle (θ) in [degrees](/source/Degree_(angle)), and the [Y-axis](/source/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](/source/Four-stroke) [camshaft](/source/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.

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Adapted from the Wikipedia article [Kramer graph](https://en.wikipedia.org/wiki/Kramer_graph) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Kramer_graph?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.