# Relative Ratio

Calculate relative atmospheric ratios

## Library

Flight Parameters

## Description

The Relative Ratio block computes the relative atmospheric ratios, including relative temperature ratio (θ), $\sqrt{\theta }$, relative pressure ratio (δ), and relative density ratio (σ).

θ represents the ratio of the air stream temperature at a chosen reference station relative to sea level standard atmospheric conditions.

`$\theta =\frac{T}{{T}_{0}}$`

δ represents the ratio of the air stream pressure at a chosen reference station relative to sea level standard atmospheric conditions.

`$\delta =\frac{P}{{P}_{0}}$`

σ represents the ratio of the air stream density at a chosen reference station relative to sea level standard atmospheric conditions.

`$\sigma =\frac{\rho }{{\rho }_{0}}$`

The Relative Ratio block icon displays the input units selected from the Units list.

## Parameters

Units

Specifies the input units:

UnitsTstaticPstaticrho_static
`Metric (MKS)`KelvinPascalKilograms per cubic meter
`English`Degrees RankinePound force per square inchSlug per cubic foot

Theta

When selected, the θ is calculated and static temperature is a required input.

Square root of theta

When selected, the $\sqrt{\theta }$ is calculated and static temperature is a required input.

Delta

When selected, the δ is calculated and static pressure is a required input.

Sigma

When selected, the σ is calculated and static density is a required input.

## Inputs and Outputs

InputDimension TypeDescription

First

Contains the Mach number.

Second

Contains the ratio between the specific heat at constant pressure (Cp) and the specific heat at constant volume (Cv). For example, (γ = Cp/Cv).

Third

Contains the static temperature.

Fourth

Contains the static pressure.

Fifth

Contains the static density.

OutputDimension TypeDescription

First

Contains the θ.

Second

Contains the $\sqrt{\theta }$.

Third

Contains the δ.

Fourth

Contains the σ.

## Assumptions

For cases in which total temperature, total pressure, or total density ratio is desired (Mach number is nonzero), the total temperature, total pressure, and total densities are calculated assuming perfect gas (with constant molecular weight, constant pressure specific heat, and constant specific heat ratio) and dry air.

## Reference

Aeronautical Vestpocket Handbook, United Technologies Pratt & Whitney, August, 1986.