Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio Calculator

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✖Maximum concentration ratio is the maximum value of the ratio of effective aperture area to absorber area.ⓘ Maximum concentration ratio [C_m]

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✖Acceptance angle is defined as the angle over which beam radiation may deviate from normal to the aperture plane and yet reach the observer.ⓘ Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio [θ_a]

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Formula

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Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio

Formula

`"θ"_{"a"} = (acos(1-2/"C"_{"m"}))/2`

Example

`"54.73561°"=(acos(1-2/"1.5"))/2`

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Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Acceptance Angle = (acos(1-2/Maximum concentration ratio))/2
θ_a = (acos(1-2/C_m))/2
This formula uses 2 Functions, 2 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

Acceptance Angle - (Measured in Radian) - Acceptance angle is defined as the angle over which beam radiation may deviate from normal to the aperture plane and yet reach the observer.
Maximum concentration ratio - Maximum concentration ratio is the maximum value of the ratio of effective aperture area to absorber area.

STEP 1: Convert Input(s) to Base Unit

Maximum concentration ratio: 1.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_a = (acos(1-2/C_m))/2 --> (acos(1-2/1.5))/2

Evaluating ... ...

θ_a = 0.955316618124509

STEP 3: Convert Result to Output's Unit

0.955316618124509 Radian -->54.7356103172556 Degree (Check conversion here)

FINAL ANSWER

54.7356103172556 ≈ 54.73561 Degree <-- Acceptance Angle

(Calculation completed in 00.004 seconds)

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< 23 Concentrating Collectors Calculators

Useful heat gain when collector efficiency factor is present

Go Useful heat gain = (Mass Flowrate*Molar Specific Heat Capacity at Constant Pressure)*(((Concentration ratio*Flux absorbed by plate)/Overall loss coefficient)+(Ambient Air Temperature-Inlet fluid temperature flat plate collector))*(1-e^(-(Collector Efficiency Factor*pi*Outer diameter of absorber tube*Overall loss coefficient*Length of Concentrator)/(Mass Flowrate*Molar Specific Heat Capacity at Constant Pressure)))

Heat removal factor concentrating collector

Go Collector heat removal factor = ((Mass Flowrate*Molar Specific Heat Capacity at Constant Pressure)/(pi*Outer diameter of absorber tube*Length of Concentrator*Overall loss coefficient))*(1-e^(-(Collector Efficiency Factor*pi*Outer diameter of absorber tube*Overall loss coefficient*Length of Concentrator)/(Mass Flowrate*Molar Specific Heat Capacity at Constant Pressure)))

Heat removal factor in compound parabolic collector

Go Collector heat removal factor = ((Mass Flowrate*Molar Specific Heat Capacity at Constant Pressure)/(Absorber Surface Width*Overall loss coefficient*Length of Concentrator))*(1-e^(-(Collector Efficiency Factor*Absorber Surface Width*Overall loss coefficient*Length of Concentrator)/(Mass Flowrate*Molar Specific Heat Capacity at Constant Pressure)))

Useful heat gain rate in concentrating collector when concentration ratio is present

Go Useful heat gain = Collector heat removal factor*(Concentrator Aperture-Outer diameter of absorber tube)*Length of Concentrator*(Flux absorbed by plate-(Overall loss coefficient/Concentration ratio)*(Inlet fluid temperature flat plate collector-Ambient Air Temperature))

Useful heat gain in compound parabolic collector

Go Useful heat gain = Collector heat removal factor*Concentrator Aperture*Length of Concentrator*(Flux absorbed by plate-((Overall loss coefficient/Concentration ratio)*(Inlet fluid temperature flat plate collector-Ambient Air Temperature)))

Flux absorbed in compound parabolic collector

Go Flux absorbed by plate = ((Hourly beam component*Tilt Factor for Beam Radiation)+(Hourly Diffuse Component/Concentration ratio))*Transmissivity of Cover*Effective reflectivity of concentrator*Absorptivity of Absorber Surface

Instantaneous collection efficiency of concentrating collector

Go Instantaneous Collection Efficiency = Useful heat gain/((Hourly beam component*Tilt Factor for Beam Radiation+Hourly Diffuse Component*Tilt factor for diffused radiation)*Concentrator Aperture*Length of Concentrator)

Useful heat gain when collection efficiency is present

Go Useful heat gain = Instantaneous Collection Efficiency*(Hourly beam component*Tilt Factor for Beam Radiation+Hourly Diffuse Component*Tilt factor for diffused radiation)*Concentrator Aperture*Length of Concentrator

Collector efficiency factor for compound parabolic collector

Go Collector Efficiency Factor = (Overall loss coefficient*(1/Overall loss coefficient+(Absorber Surface Width/(Number of Tubes*pi*Inner diameter absorber tube*Heat Transfer Coefficient Inside))))^-1

Area of Aperture given Useful Heat Gain

Go Effective area of aperture = Useful heat gain/(Flux absorbed by plate-(Overall loss coefficient/Concentration ratio)*(Average temperature of absorber plate-Ambient Air Temperature))

Collector efficiency factor concentrating collector

Go Collector Efficiency Factor = 1/(Overall loss coefficient*(1/Overall loss coefficient+Outer diameter of absorber tube/(Inner diameter absorber tube*Heat Transfer Coefficient Inside)))

Instantaneous collection efficiency of concentrating collector on basis of beam radiation

Go Instantaneous Collection Efficiency = Useful heat gain/(Hourly beam component*Tilt Factor for Beam Radiation*Concentrator Aperture*Length of Concentrator)

Area of absorber in central receiver collector

Go Area of Absorber in Central Receiver Collector = pi/2*Diameter of Sphere Absorber^2*(1+sin(Rim Angle)-(cos(Rim Angle)/2))

Area of Absorber given Heat Loss from Absorber

Go Area of absorber plate = Heat Loss from Collector/(Overall loss coefficient*(Average temperature of absorber plate-Ambient Air Temperature))

Concentration ratio of collector

Go Concentration ratio = (Concentrator Aperture-Outer diameter of absorber tube)/(pi*Outer diameter of absorber tube)

Inclination of reflectors

Go Inclination of Reflector = (pi-Tilt Angle-2*Latitude Angle+2*Declination Angle)/3

Solar Beam Radiation given Useful Heat Gain Rate and Heat Loss Rate from Absorber

Go Solar beam radiation = (Useful heat gain+Heat Loss from Collector)/Effective area of aperture

Useful heat gain in concentrating collector

Go Useful heat gain = Effective area of aperture*Solar beam radiation-Heat Loss from Collector

Outer Diameter of Absorber Tube given Concentration Ratio

Go Outer diameter of absorber tube = Concentrator Aperture/(Concentration ratio*pi+1)

Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio

Go Acceptance Angle = (acos(1-2/Maximum concentration ratio))/2

Maximum possible concentration ratio of 3-D concentrator

Go Maximum concentration ratio = 2/(1-cos(2*Acceptance Angle))

Acceptance Angle of 2-D Concentrator given Maximum Concentration Ratio

Go Acceptance Angle = asin(1/Maximum concentration ratio)

Maximum possible concentration ratio of 2-D concentrator

Go Maximum concentration ratio = 1/sin(Acceptance Angle)

Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio Formula

Acceptance Angle = (acos(1-2/Maximum concentration ratio))/2
θ_a = (acos(1-2/C_m))/2

What is concentration ratio?

The concentration ratio is defined as the ratio of the effective area of aperture to the surface area of the absorber.

How to Calculate Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio?

Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio calculator uses Acceptance Angle = (acos(1-2/Maximum concentration ratio))/2 to calculate the Acceptance Angle, The Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio formula is defined as the angle over which beam radiation may deviate from normal to the aperture plane and yet reach the observer. Acceptance Angle is denoted by θ_a symbol.

How to calculate Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio using this online calculator? To use this online calculator for Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio, enter Maximum concentration ratio (C_m) and hit the calculate button. Here is how the Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio calculation can be explained with given input values -> 3136.119 = (acos(1-2/1.5))/2.

FAQ

What is Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio?

The Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio formula is defined as the angle over which beam radiation may deviate from normal to the aperture plane and yet reach the observer and is represented as θ_a = (acos(1-2/C_m))/2 or Acceptance Angle = (acos(1-2/Maximum concentration ratio))/2. Maximum concentration ratio is the maximum value of the ratio of effective aperture area to absorber area.

How to calculate Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio?

The Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio formula is defined as the angle over which beam radiation may deviate from normal to the aperture plane and yet reach the observer is calculated using Acceptance Angle = (acos(1-2/Maximum concentration ratio))/2. To calculate Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio, you need Maximum concentration ratio (C_m). With our tool, you need to enter the respective value for Maximum concentration ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Acceptance Angle?

In this formula, Acceptance Angle uses Maximum concentration ratio. We can use 1 other way(s) to calculate the same, which is/are as follows -

Acceptance Angle = asin(1/Maximum concentration ratio)

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