Ragnall may have been the father of Echmarcach mac Ragnaill, King of Dublin and the Isles.
Other possible parents of this Norse-Gaelic monarch include two like-named rulers of Waterford: Ragnall mac Ímair, King of Waterford, and this man's apparent son, Ragnall ua Ímair, King of Waterford.
Echmarcach appears to first emerge in the historical record in the first half of the eleventh century when the ninth- to twelfth-century Anglo-Saxon Chronicle reveals that he was one of the three kings who met with Knútr Sveinnsson, ruler of the North Sea Empire comprising the kingdoms of Denmark, England, and Norway.
This source's record of Echmarcach in company with Máel Coluim and Mac Bethad mac Findlaích—the two other named kings—could indicate that he was in some sense a 'Scottish' ruler, and that his powerbase was located in the Isles.
Such an orientation could add weight to the possibility that Echmarcach was descended from Ragnall.
If Hákon had indeed possessed overlordship of the Isles, his eventual demise in 1029 or 1030 may well have paved the way for Echmarcach's own rise to power.

There is evidence to suggest that Ragnall had a daughter who married into the Uí Briain.
Specifically, in 1032, the Annals of Inisfallen states that Donnchad mac Briain, King of Munster married the daughter of a certain Ragnall, adding: "hence the saying: 'the spring of Ragnall's daughter'".
Upon her death about two decades later, the Annals of Tigernach identifies this woman as Cacht ingen Ragnaill, and styles her Queen of Ireland.
Like Echmarcach himself, Cacht's patronym could be evidence that she was a daughter of Ragnall, or a near relation of the like-named men who ruled Waterford.

Ragnall may have also been the paternal grandfather of Gofraid mac Amlaíb meic Ragnaill, King of Dublin.
The latter's apparent father, Amlaíb, could well have been the father of Sitriuc mac Amlaíb, a man whose fall in an attack on Mann with two members of the Uí Briain is recorded by the Annals of Ulster in 1073.
Decades afterwards in 1087, the same source relates that two descendants of a certain Ragnall were slain in another invasion of Mann.
Whilst Amlaíb may have been the father of these two as well, it is also possible that they were sons of Echmarcach or Gofraid mac Amlaíb meic Ragnaill.
Ragnall may have been the father of Echmarcach mac Ragnaill, King of Dublin and the Isles. Other possible parents of this Norse-Gaelic monarch include two like-named rulers of Waterford: Ragnall mac Ímair, King of Waterford, and this man's apparent son, Ragnall ua Ímair, King of Waterford. Echmarcach appears to first emerge in the historical record in the first half of the eleventh century when the ninth- to twelfth-century Anglo-Saxon Chronicle reveals that he was one of the three kings who met with Knútr Sveinnsson, ruler of the North Sea Empire comprising the kingdoms of Denmark, England, and Norway. This source's record of Echmarcach in company with Máel Coluim and Mac Bethad mac Findlaích—the two other named kings—could indicate that he was in some sense a 'Scottish' ruler, and that his powerbase was located in the Isles. Such an orientation could add weight to the possibility that Echmarcach was descended from Ragnall. If Hákon had indeed possessed overlordship of the Isles, his eventual demise in 1029 or 1030 may well have paved the way for Echmarcach's own rise to power.
There is evidence to suggest that Ragnall had a daughter who married into the Uí Briain. Specifically, in 1032, the Annals of Inisfallen states that Donnchad mac Briain, King of Munster married the daughter of a certain Ragnall, adding: "hence the saying: 'the spring of Ragnall's daughter'". Upon her death about two decades later, the Annals of Tigernach identifies this woman as Cacht ingen Ragnaill, and styles her Queen of Ireland. Like Echmarcach himself, Cacht's patronym could be evidence that she was a daughter of Ragnall, or a near relation of the like-named men who ruled Waterford.
Ragnall may have also been the paternal grandfather of Gofraid mac Amlaíb meic Ragnaill, King of Dublin. The latter's apparent father, Amlaíb, could well have been the father of Sitriuc mac Amlaíb, a man whose fall in an attack on Mann with two members of the Uí Briain is recorded by the Annals of Ulster in 1073. Decades afterwards in 1087, the same source relates that two descendants of a certain Ragnall were slain in another invasion of Mann. Whilst Amlaíb may have been the father of these two as well, it is also possible that they were sons of Echmarcach or Gofraid mac Amlaíb meic Ragnaill.
Ragnall mac Gofraid