The scene is as evocative, as quintessentially American as a Norman Rockwell painting: noisy schoolchildren on an autumn evening in the park opposite where I live, assembled for sports practice. Only one element jars - the helmets and bulky shoulder padding worn by these diminutive athletes, as their instructor takes them through a routine of sprints and tackles. But whatever the contrast with the innocence of the moment, no coach or parent would have it otherwise. Such is the reality of the troubled sport of American football.

Football is still this country's most popular sport. It commands the biggest television audiences, and its showcase, the National Football League, claims to be the richest in the world. But behind the brash, opulent facade, all is not well.

Last month, the sport's high command moved to quell uproar among players by preventing Rush Limbaugh - the conservative radio host who in the past has made disparaging remarks about black players - from buying a stake in an NFL team. More ominously, for the first time I can remember, you see empty seats at games that in past years would have been sold out. Long imagined to be recession-proof, pro football is feeling the pinch too.

But in the long term, most alarming of all is the reason why those children in the park - none of them more than 12 years old - were kitted out like medieval knights girded for battle. Even the most casual observer can't watch a game for 10 minutes without realising that gridiron football is a brutal business.

And it has ever been so; back in 1905, well before the NFL was invented, President Theodore Roosevelt called an emergency meeting at the White House, worried at how "the brutality of the prize ring had invaded college football".

The sport may leave foreigners cold, but what Americans call football (despite the fact it is a handling and throwing game in which foot almost never makes contact with ball) is as American as apple pie. Indeed, some say it is a perfect metaphor for national life: a ritual swamped in statistics, with tedious, endless confabulating punctuated by brief moments of violence. Alas, that violence can have devastating long-term consequences.

In September, the University of Michigan published a survey (paid for by the league) of more than 1,000 former players, who had all put in a minimum of three seasons. The study found that among those over 50, dementia, Alzheimer's and other memory-related diseases were five times higher than the national average, while for younger retired players the incidence was 19 times greater.

The NFL and others have challenged the reliability of the figures, but anecdotal evidence from physicians and other research points to an identical conclusion. Ever more cases are also coming to light of ex-players suffering from the separate condition of CTE, or chronic traumatic encephalopathy. They are, in plain English, "punch-drunk," like a boxer who's hung around the ring too long.

The perils of football lie not just in the "hits" that thrill fans, and to which entire websites are devoted. There are also banned practices such as helmet-to-helmet collisions and "spearing" (when the helmet is used as a weapon). The concussions that can follow are highly dangerous, especially if not acted upon at once. In the NFL they now usually are - but not necessarily in football at secondary school level, where most serious playing careers begin. In the decade to 2007, according to The New York Times, at least 50 high school players and younger were killed or seriously hurt by head injuries. These were not always major concussions, but smaller "sub-concussions", less easily noticed but which can cause irreparable damage to the less-developed brain tissue of teenage players.