## 1 Introduction  
Pressure effects on flame spread over solids has been studied for several decades to provide guidance for fire protection in aircraft and high-altitude buildings. For example, in China, one of the interests is based on the fire safety research for important historical or Buddhism buildings in the Qinghai-Tibet plateau. As the essential parameter related to oxidation and flow in combustion, pressure was confirmed to have obvious influences on fire spreading behavior and burning characteristics for solid fuels, e.g., wood [1; 2; 3; 4], rigid polyurethane (RPU) foam [5; 6], flexible polyurethane (FPU) foam [7; 8; 9], extruded polystyrene (XPS) [10; 11], or other polymers [12; 13; 14]. Nowadays, more attentions are paid to fire behavior of these materials because of rapid development in the construction industry.  
The most classical theoretical modeling about pressure vs. flame spread could be traced back to the Pressure Modeling of Fires by [PERSON] [1] in 1973, which showed a concise and important correlation for flame spread over solids with various pressures by simplified dimensional analysis as \(V_{p}\propto p^{2/3}\). Subsequently in 2000, a further developed theory also by [PERSON] et al. known as Radiation FireModeling [2] was proposed to give a deeper insight into pressure effects on detailed heat and the mass transfer process. However, limitations of theoretical modellings still exist as the complexity of real fire scenarios with various combustibles and developing processes, i.e., extensive investigation of pressure effects on fire spreading and burning behavior for solid combustibles is meaningful.  
Another key parameter is the inclination of flame spreading surface, indicating intense correlations with flame spread rate (FSR), fire configuration, etc., particularly. As early as 1992, upward fire propagation over inclined PMMA slab surface was studied experimentally by [PERSON] and [PERSON] [13], which reported the clear difference of spread for thin and thick fuels under different inclinations. Later, an important early semi-empirical model of upward flame spread with an orientation effect was proposed by [PERSON] in 2001 using a polyethylene terephthalate (PET) board [14]. In addition, related works were conducted continuously by [PERSON] et al. [15; 16] in recent years. However, it will be a different story when both effects of inclination and pressure are combined, complexly impacting the entire spreading process. Research studies referring to the coupling effects were mostly focused on phenomenological fire behavior changes at high altitude by experimental studies, e.g., [4; 6; 8]. Additionally, downward spreading tests over FPU board at various inclinations under sub-atmospheric pressures were performed in our latest work [9]. It was found that preheating mechanism variation, strongly dependent on the coupling effects and surface materials, would play an important part in flame spread. As a result of the complication in fuel types and forms mentioned, it is worth a more extensive exploration of this issue.  
Within this paper, as a further investigation of our previous work in [9], both experimental and theoretical study were conducted to show a relatively full comparison of downward and upward flame spreading processes over FPU foam board with four inclination angles under three decreased pressures. Burning characteristics including flame spread rate (FSR), burning rate and flame morphology are concentrated to reveal the complicated influences of pressure and orientation. Semi-qualitative relationships of the coupling effects were formulated by overall theoretical analysis of heat transfer mechanisms. This work could be helpful for fire safety engineering design of buildings at high altitudes.