What is transubstantiation? According to Wikipedia:


  When at his Last Supper, Jesus said: "This is my body", what he held in his hands still had all the appearances of bread: these "accidents" remained unchanged. However, the Roman Catholic Church believes that, when Jesus made that declaration, the underlying reality (the "substance") of the bread was converted to that of his body. In other words, it actually was his body, while all the appearances open to the senses or to scientific investigation were still those of bread, exactly as before.


and also


  The Catholic Church holds that the same change of the substance of the bread and of the wine occurs at the consecration of the Eucharist


http://en.wikipedia.org/wiki/Transubstantiation

So, how can the Eucharist change from bread to body if it is not measurably altered in any way? How is it different from saying that it doesn't change at all? Is it an allegory? If not, how does it change in practical terms?
Transubstantiation relies on the Aristotelian distinction between essence and accidents. From the linked Wikipedia article:


  Catholic theologians such as Thomas Aquinas have employed the
  Aristotelian concepts of substance and accident in articulating the
  theology of the Eucharist, particularly the transubstantiation of
  bread and wine into body and blood. According to this tradition, the
  accidents of the bread and wine do not change, but their substances
  change from bread and wine to the Body and Blood of Christ.


The "measurable" properties you are referring to (taste, feel, etc.) are accidental properties, not the substance of the bread/wine.