Scaled Impulse at Altitude 'z' v1

The Scaled Impulse at Altitude calculator estimates the scaled impulse of an explosion at an altitude (z) based on the temperature and pressure at the altitude and the ambient temperature and pressure. 

INSTRUCTIONS: Choose units and enter the following:

• (pz) Pressure at Altitude z
• (po) Ambient Pressure
• (to) Ambient Temperature
• (tz) Temperature at Altitude z

Scaled Impulse at Altitude (SIA_z): The impulse magnitude is returned in kilogram-meters per second (kg·m/s).  However, these can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Scaled Impulse at Altitude 'z' computes impulse using the ambient pressure, ambient temperature, pressure at the 'z' altitude and temperature at the 'z' altitude. This equation is part of Sachs scaling law.

The formula for Scaled Impulse at Altitude used in this calculator is:

SIA = (po / pz)^2/3 ⋅ (to/tz)^1/2

where:

• SIA = Scaled Impulse at Altitude
• po = Ambient Pressure
• pz = Pressure at Altitude z
• to = Ambient Temperature
• tz = Temperature at Altitude z

The Scaled Impulse at Altitude 'z' computes impulse using the ambient pressure, ambient temperature, pressure at the 'z' altitude and temperature at the 'z' altitude. This equation is part of Sachs scaling law.

To see the second version of this equation, click here.

About Sachs Scaling Law

In the case of blast waves from explosions produced at altitude, where ambient conditions can be very different from those at sea level, the most commonly used scaling law is that due to Sachs. The application of the Sachs scaling law leads to the formulation of altitude scaling factors.

Resource:

• "Formulae for Ammunition Management." International Ammunition Technical Guideline. 1st ed. New York: UN, 2013. 2-3.UN SaferGuard. United Nations Office for Disarmament Affairs (UNODA), 20 May 2013. Web. 12 June 2015. <http://www.un.org/disarmament/convarms/Ammunition>.