Its all about Conserving Energy How predictive rendering can avoid creating an accidental Death Ray Ian Williams, Director of Applied Engineering, NVIDIA
The Problem A Quick Physics Recap Simulating the Death Ray in Iray Agenda Deriving Temperature from Irradiance Comparing Predictions with Measurement Conclusions 2
The Problem August 29 th 2013 Martin Lindsay parked his Jaguar car on Eastcheap, London around noon 2 hours later he returned to find parts of the car had melted 3
The Scale of the Problem “ On Tuesday afternoon, I was sent out to see if I could fry an egg in the heat, a task that I presumed was impossible on an overcast September day. But, not only was it possible, I had to run out of the death ray that was slowly cooking my egg, because the thinning hairs on my head started to catch fire. ” “ On Monday, the air temperature in the concentrated beam, reached 69.8C, which in old money is 158F. To put that in context, the world’s hottest temperature was recorded in Death Valley at 56.7C (134F) over a century ago .” 4
Death Ray’s Apparently are Fairly Common 5
A Quick Physics Recap Agenda 6
Electromagnetic Radiation A Quick Recap Electromagnetic Radiation consists of waves that are synchronized oscillations of electric and magnetic fields that propagate at the speed of light Produced whenever charged particles are accelerated, and these waves can subsequently interact with any charged particles EM waves carry energy, momentum and angular momentum away from their source particle and can impart those quantities to matter with which they interact Electromagnetic spectrum: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays 7
How Does Sunlight Heat Things Up? Three Main Modes of Energy Transfer Radiation is both absorbed and emitted Convection Conduction 8
Governing Laws The law of conservation of energy states: That the total energy of an isolated system is constant; energy can be transformed from one form to another, but cannot be created or destroyed The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems, and states: That the change in the internal energy of a closed system is equal to the amount of heat supplied to the system, minus the amount of work done by the system on its surroundings 9
Quantifying Energy Transfer in the Electro Magnetic Spectrum Irradiance Radiant Flux per unit area received by a Surface Units = watts per square metre W/m2 Hemispherical quantity 10
Solar Irradiance and Atmospheric Absorbtion Irradiance The electromagnetic radiation emitted by the sun incident on the top of the atmosphere 50% in region beyond visible light 40% in visible light region 10% in ultraviolet region On a clear day approximately 50% of solar energy absorbed by atmosphere 11
Simulating the Death Ray in Iray Agenda 12
Simulating the Physics of the Death Ray Iray Walkie Talkie Building and Environment were extensively modelled in detail using AutoDesk 3D Studio Max Used Iray Renderer to: Simulate time of day and year using calibrated Sunlight model Calculate Irradiance incident on specific surface 13
The Model 20 Fenchurch Street and Surroundings, London Movie 14
Time of Day Analysis 29 August 2013 Movie 15
Predicted Irradiance from Iray 29 August 2013 Movie 16
The Energy Contained in the Death Ray Direct Sunlight on a clear day has an Irradiance of ~110K Lux or ~1.1 KW/m 2 Predicted Irradiance at street level outside the Death Ray was ~98K Lux or ~1.1 KW/m 2 Predicted Irradiance at street level inside the Death Ray was ~700K Lux or ~7.5 KW/m 2 =6x more powerful than the Sun! 17
It Could Have Been Worse... Slight modifications to the building geometry, in the form of between 5 to 10 degrees more curvature, increased Irradiance from: ~700K Lux or ~7.5 KW/m 2 To ~3M Lux or ~32.3 KW/m 2 =30x more powerful than the Sun!!! 18
Agenda Deriving Temperature from Irradiance 19
Calculating Temperature from Irradiance Solar Heat Transfer to a Surface 20
Temperature of the Surface Energy Balance Assuming system is steady state with no phase changes, then from 1 st law of thermodynamics the energy balance equation is: E e . α = ε . σ [ T 4 - T 4 ] + h surf-air [T surf-air – T air-amb ] + k . [T surf-air – T surf-other ] / s surf-air air-amb Surf -> Atmosphere Atmosphere -> Surf Energy transfer Energy transfer Absorbed Re-Radiated through Convection Through Conduction Energy Energy E e = Irradiance (Wm- 2 ) h surf-air = Heat transfer coefficient α = Absorptivity between surface ε = Emissivity and air (Wm- 2 K -1 ) σ = Stefan-Boltzman constant = 5.670373x10 -8 (Wm -2 K -4 ) k = Thermal Conductivity of T surf-air = Temperature at air surface boundary (K) surface material (Wm- 1 K -1 ) T air-amb = Ambient air temperature (K) s = Surface material thickness T surf-other = Temperature at other side of surface (K) 21
Simplifying Things Assume worst case scenario where energy transfer/cooling through conduction is negligible Assume radiation from atmosphere back to surface can be considered negligible Energy Transfer Equation be re-written: E e . α - ε . σ T 4 - h surf-air [T surf-air – T air-amb ] = 0 surf-air Which equals: ε . σ . T 4 + h surf-air .T surf-air – [ E e . α + h surf-air .T air-amb ] = 0 surf-air Which is a quartic of the form: a = ε . σ d = h surf-air a . x 4 + b . x 3 + c . X 2 + d .x – e = 0 e = E e . α + h surf-air .T air-amb 22
General Solution To A Quartic Equation 23
In Our Case… b = c = 0 24
So The Formula Becomes… Δ 0 = 12ae Where: Δ 1 = 27ad 2 a = ε . σ d = h surf-air Q = [ ( Δ 1 + ( Δ 1 2 - 4 Δ 0 3 ) 1/2 )/2] 1/3 e = E e . α + h surf-air .T air-amb + ε . σ .T 4 air-amb S = ½ [ (1/3a) * (Q + Δ 0 /Q) ] 1/2 q = d/a x 1,2 = -S ± ½( -4S 2 + q/S ) 1/2 x 3,4 = S ± ½( -4S 2 – q/S ) 1/2 T surf-air = X 1 or X 2 or X 3 or X 4 Depending on which root is a +ve real number 25
Assumed Values… E e = Irradiance (Wm- 2 ) P (W) = E v(lx) × A (m 2 ) / η (lm/W) , where η = Lumic Efficacy = 0.93 for sunlight α = Absorptivity Absorptivity Emissivity Asphalt 0.93 0.93 ε = Emissivity Polished Aluminum 0.09 0.09 Magnesium Oxide Paint 0.09 0.09 σ = Stefan-Boltzman constant = 5.670373x10 -8 Wm -2 K -4 Chromium 0.2 0.2 Sherwin Williams White Paint 0.89 0.87 T surf-air = Temperature at air surface boundary (K) Concrete 0.6 0.88 Red Brick 0.94 0.93 T air-amb = Ambient air temperature (K) = 300K Polythene Black Plastic 0.94 0.92 Black Paint 0.94 0.94 h surf-air = Heat transfer coefficient between surface and air (Wm- 2 K -1 ) Human Skin 0.97 0.97 (source engineering toolbox) = 10.45 – v + 10v 1/2 , where v is velocity of object in air (source engineering toolbox) = 10.45 Wm- 2 K -1 for static object 26
Calculated Temperatures Ambient Temperature = 27C, 80F NORMAL INSIDE SUNLIGHT DEATH RAY Asphalt 82C, 179F 276C, 530F Asphalt Light Breeze 57C, 135F 208C, 407F Black Plastic 82C, 179F 277C, 531F Black Plastic Light Breeze 58C, 136F 209C, 408F Chrome 44C, 113F 146C, 295F Chrome Light Breeze 34C, 94F 82C, 180F 27
Melting Point of Plastics Material Degrees(F) Material Degrees(F) Acetal (CoPo) 400 PBT 500 Acetal (HoPo) 425 PCT 580 Acrylic 425 Peek 720 Acrylic (Mod) 500 PET 540 ABS (MedImp) 400 Polycarbonate 550 ABS (HiImpFR) 420 Polyetherimide 700 CelAcetate 385 Polyethylene (LD) 325 CelButyrate 350 Polyethylene (HD) 400 CelPropionate 350 Polypropylene 350 EVA 350 Polystyrene (GP) 350 LCP 500 Polystyrene (MI) 380 Nylon (6) 500 Polystyrene (HI) 390 Nylon (6/6) 525 Polysulfone 700 Polyamide-imide 650 PPO 575 Polyarylate 700 PVC (Rig/Flex) 350/325 TFE 600 Source: http://plastictroubleshooter.com/ThePlasticTroubleshooter/melt_temps.htm 28
Observations on Calculated Temperatures Some temperatures seem believable, eg: Chrome in Normal Sunlight – 44C, 134F Ashpalt in Light Breeze – 57C, 135F Some temperatures too high, eg: Asphalt in the Death Ray – 276C, 530F Asphalt in a Light Breeze - 208C, 407F Conclusion energy transfer model is too simplistic As energy transfer from Irradiance increases Reality will be greater dissipation through Convection and Conduction 29
Agenda Comparing Predictions with Measurement 30
Calibration Scene 31
Calibration Scene in Iray 32
Physical Measurements 33
Comparing Measured and Calculated Temperature Ambient Temperature = 71F, Windspeed ~0 Knots CALCULATED MEASURED MEASURED FROM 3-11-2015 3-11-2015 IRRADIANCE 1:05 PM 1:51 PM* 1 Asphalt (Horizontal) 122F 106F 87F 2 Concrete (Horizontal) 108F 98F 87.5F 3 Concrete (Vertical, ~south) 116F 104F 89F 4 White Painted Steel (Vertical, ~south) 130F 86.5F 76F 5 White Painted Steel (Vertical, ~east) 66F 78.5F 74.5F 6 Black Painted Steel (Vertical, ~south) 131F 99F 80F 7 Black Painted Steel (Vertical, ~east) 114F 92.5F 80F * Full Cloud Cover for > 30 mins 34
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