A scientific experience with the flight of MUSEO AERO SOLAR
November 1, 2009 § Leave a comment
written by Saverio Tozzi, Centro di Scienze Naturali, Comune di Prato
I have been invited to follow an experience of MUSEO AERO SOLAR, held in Carmignano, Parco Quinto Martini, on Sunday October 4th 2009.
The following principles allow for the museo’s flight: first of all Archimedes’ law, dating back to the 3rd century b.C., whose simplest assertion states that “a body in a fluid is lifted upwards proportionally to the weight of the fluid it displaces”. Widely known for its application to liquids, the principle nonetheless holds of all fluids, including air. It is actually the weight difference between the warm mass of air within the balloon and the mass of external, colder and hence heavier air, that allows its upwards lift and accounts for the possibility of lifting the wrapping alongside whatever it is hanging from it. In conventional hot air balloons, warmed by a gas heater, internal air temperature reaches around 120 °C: but how warm will it get through sunshine alone? And how can the density difference between internal and external air be measured?
This can be answered by the law of perfect gases, expressing in a constant the relation between pressure, volume and temperature. Rigorously speaking air is not a perfect gas; nonetheless this degree of approximation will not be relevant when dealing with the measurements involved in this experiment. We’ll moreover assume, to calculate the balloon’s lift, that external and internal air has the same pressure; this could be justified by the wrapping’s extremely low resistance. The equation will then be:
Where P is pressure measured in Pascal, V is the volume in cube meters, T is the temperature in Kelvin degrees, n is the number of gas moles, and R is a constant whose value for dry air is 287 J/ kg*K. This value induces a marginal error since air will presumably contain a variable quantity of water vapour which will slightly alter it. The equation can be written as: Where R is air density expressed in kg/m3. It is immediately evident that density grows proportionally to pressure P and inversely to temperature T. The balloon’s lift can hence be easily obtained, in kg, by multiplying the difference in density between internal and external air, expressed in kg/m3, by the volume of the balloon itself.
From theory to practice
We have been able to gather data on this experience by installing a weather station at ground level to keep track of temperature, humidity and air pressure; wind speed and direction have been measured 8 meters above ground to avoid surrounding obstacles. The balloon’s inflation has begun around 6.40 am, at an external temperature of 12 °C, relative humidity of 53%, and atmospheric pressure of 1011 hPa. The wind has been calm throughout the whole experience. The balloon’s inner temperature has been constantly monitored by a radio-controlled sensor. MUSEO AERO SOLAR’s current circumference is almost 70 meters. Since its shape is only approximately spherical, its estimated volume is of around 3500 m3; this has subsequently been confirmed by experimental data. The balloon was fully inflated at 8.17 am; the pipe connecting it to fans was sealed closed. At the location’s latitude the sun should have risen at 7.14 am, but the presence of natural obstacles postponed effective sunrise to 7.39 am; the sun then started to warm the balloon up. At 8.39 am MUSEO AERO SOLAR lifted itself from the ground; its floating lift was then obviously higher then the wrapping’s weight, which was around 75 kg.
After slowly rising up to around 50 meters above ground, adequately anchored, the balloon was drawn back to earth, ending its flight at 9.21 am.
The following graph plots external temperature, internal temperature, and lift – as determined by the aforementioned parameters.
We can now analyse the three curves. External temperature, following its natural course determined by sunshine, has risen in an almost constant progression, climbing from the initial 13.2 °C to 17.7 °C as measured at 9.30 am.
The progression of internal temperature is more interesting to discuss; it has constantly risen until the flight’s height peak, to subsequently stabilise around 24 °C. This induces a variety of remarks. First of all we know that air, being transparent to sun-rays, isn’t warmed by direct exposure to light, but through its contact with land – this is also why temperature drops at higher altitudes. For the same reason air inside the balloon got warmer trough its contact with the wrapping’s polyethylene surface, which itself was heated by the sun in an uneven fashion according to its varying colour.
We should then presume that, although we measured external air temperature at ground level, the air immediately around the balloon should be cooler. The curve’s plateau then represents an equilibrium point between the sun’s warming of the inner air and the heat dispersion induced by the wrapping’s contact with cooler outside air. It should be remarked that the sensor was placed on the inner side of the balloon’s surface, and therefore was particularly sensitive to this effect.
The lift curve is valid for its initial part, but becomes less representative and undoubtedly under-estimated after the balloon reaches 50 meters of altitude. First of all, air pressure gradually decreases by an average of 11 hPa every 100 m: air will then be slightly less dense at that height, hence reducing the balloon’s lift. This effect, however, has little quantitative relevance. On the other hand, the error implied by the comparison between the balloon’s internal temperature and the air’s temperature at ground level (which, as we have seen, is warmer then at 50 meters of altitude) is of a wholly appreciable scale. At 50 meters above ground air, being colder and denser, is heavier. This error is further enhanced by the sensor’s positions on the wrapping, which makes its findings scarcely representative of the whole balloon’s inner air condition. It is hence very likely the balloon’s absolute lift has reached slightly higher values then the graph’s 120 kg. This hypothesis is partially confirmed by the inner temperature’s rising in the landing phase; the same holds of the lift, which ultimately reaches over 130 kg.
We have seen how an experience of this kind can offer a practical representation of various principles governing natural phenomena. We have also seen how experimental measurements – even when dealing with a simple phenomenon such as this – must keep track of many different factors to reach a significant overlap between theoretical prediction and experimental data. If the experience were to be repeated, the gathering of experimental data would be dramatically improved by placing the temperature sensor at the balloon’s centre; a second sensor, mounted on the balloon’s external surface so as to measure in-flight air conditions, would also be of great use. A more precise measurement of the balloon’s lift could be obtained by applying a dynamo-meter to the balloon’s anchoring ropes.