Prototype for testing: car Mitsubishi Outlander 2014 PHEV with sustainable paint system for aircraft
Problem statement:
$$P=T·v, T\simeq D, D=\frac{1}{2}\rho v^2S_d C_D, P=D·v=\frac{1}{2}\rho v^3S_d C_D, \eta=\frac{P_s}{P_a},\eta=\frac{\alpha \epsilon ISs}{\frac{1}{2} \rho v^3SdC_D}$$
Energy equation:
$$\rho c_p\mathbf{v}·\nabla \mathbf{T}-\mathbf{v}·\nabla \mathbf{p}=\mathbf{\Phi_v}-\nabla·\mathbf{q_r}$$
Legend:
$$P=Power,T=Thrust,D=Drag,v=speed,\rho=density$$
$$Ss=solar\,surface,Sd=frontal\,surface,C_D=Drag\,Coefficient,\eta=saving$$
$$\alpha=solar\, absorptivity,\epsilon=emissivity,I=intensity~of\,solar\,radiation$$
$$P_s=P_{solar},P_a=P_{aerodynamic}$$
Saving are the Solar power divided the Aerodynamic power due to drag
| intensity of solar radiation | solar absorptivity | emissivity | air density | Drag coefficient | Dynamic viscosity |
| I | α | ε | ρ | Cd | μ |
| W/m2 | – | – | kg/m3 | – | Pa·s |
| 1000 | 0,925 | 0,885 | 1,225 | 0,33 | 1,85E-05 |
| Length | illuminance | frontal surface | solar surface | Fuel economy normal | Fuel economy improved |
| L | Ev | Sd | Ss | FN | FI |
| m | lux | m2 | m2 | L/100 km | L/100 km |
| 4,655 | 110000 | 3,024 | 4,190 | 8 | 7 |
| velocity | velocity | saving in theory | saving tested | Reynolds number |
| v | v | η | (FN-FI)/FN | Re |
| m/s | km/h | – | – | – |
| 49 | 178 | 0,046 | 1,52E+07 | |
| 33 | 120 | 0,151 | 0,125 | 1,03E+07 |
| 17,5 | 63 | 1,047 | 5,39E+06 | |
| 14,0 | 50 | 2,045 | 4,32E+06 |
For v=33 m/s, energy equation terms in W/m3:
$$\rho c_p\mathbf{v}·\nabla \mathbf{T}=8812,-\mathbf{v}·\nabla \mathbf{p}=730895,\mathbf{\Phi_v}=272727,-\nabla·\mathbf{q_r}=-22909$$
Thermal energy is negligible compared to convective terms in the energy equation. So, in first approximation we can neglect changes in temperature. Kinetic energy is used to overcome friction. Solar radiation reduces the main effect of friction(drag). Large Re numbers.
There are mainly two ways to test the innovation: In a wind tunnel or outdoors. The challenge in a wind tunnel is reproducing solar radiation, which requires special and expensive lamps with an illuminance of 110,000 lux; and also the difficulty of reproducing the real parameters of the problem. The outdoor challenge is controlling the test variables: wind, solar radiation, prototype cars, etc. to reproduce the same conditions of the tests to be compared.
For simplicity, it is proposed to do the tests outdoors. Comparing the innovation prototype fuel consumption with the same model car without the paint system.
Conclusions: Saving in theory η=15,1%, saving tested (FN-FI)/FN=12,5%. The difference may be partly due to the fact that rolling losses have not been taken into account in the calculations (theory).