Sakuma-Hattori equation

The Sakuma–Hattori Equation calculator predicts the amount of thermal radiation, radiometric flux or power emitted from a blackbody based on a scalar coefficient, Second Radiation Constant, temperature dependent wavelength and the temperature.

INSTRUCTIONS: Choose units and enter the following:

• (C) Scalar coefficient
• (λ_x)  Wavelength (temperature dependent)
• (T) Temperature

Sakuma-Hattori S(T): The calculator returns the value as a real number.  Wavelength is converted to meters and temperature converted to degrees Kelvin automatically in the calculator.

The Math / Science

The Sakuma-Hattori equation is a mathematical model for predicting the amount of thermal radiation, radiometric flux or radiometric power emitted from a perfect blackbody or received by a thermal radiation detector.The Sakuma–Hattori was first proposed by Fumihiro Sakuma, Akira Ono and Susumu Hattori in 1987.

The Sakuma–Hattori equation gives the electromagnetic signal from thermal radiation based on an object's temperature. The signal can be electromagnetic flux or signal produced by a detector measuring this radiation. It has been suggested that below the silver point[A], a method using the Sakuma–Hattori equation be used.  The Sakuma-Hattori equation is:

     `S(T) =C/(exp(C_2/(λ_x ·T))-1)`

 where:

• S(T) is the Sakuma-Hattori value.
• C is the scalar coefficient
• c₂ is the Second Radiation Constant (0.014387752 m⋅K)
• λ_x is the temperature dependent effective wavelength in meters
• T is the temperature in Kelvin

In 1996 a study investigated the usefulness of various forms of the Sakuma–Hattori equation. This study showed the Planckian form to provide the best fit for most applications. This study was done for 10 different forms of the Sakuma–Hattori equation containing not more than three fitting variables. In 2008, BIPM CCT-WG5 recommended its use for radiation thermometry uncertainty budgets below 960 C.

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